Covariant quantization: spectral analysis versus deformation theory

A. Alekseev and E. Meinrenken, The non-commutative Weil algebra, Invent. Math., 139 (2000), 135–172 A. Alekseev and E. Meinrenken, Poisson geometry and the Kashiwara–Vergne conjecture, C. R. Math. Acad. Sci. Paris, 335 (2002), 723–728 A. Alekseev and E. Meinrenken, On the Kashiwara–Vergne conjecture, Invent. Math., 164 (2006), 615–634 M. Andler, A. Dvorsky and S. Sahi, Kontsevich quantization and invariant distributions on Lie groups, Ann. Sci. École Norm. Sup. (4), 35 (2002), 371–390 M. Andler, S. Sahi and Ch. Torossian, Convolution of invariant distributions: proof of the Kashiwara–Vergne conjecture, Lett. Math. Phys., 69 (2004), 177–203 H. Aoki and T. Ibukiyama, Simple graded rings of Siegel modular forms, differential operators and Borcherds products, Internat. J. Math., 16 (2005), 249–279 J. Arazy and B. Ørsted, Asymptotic expansions of Berezin transforms, Indiana Univ. Math. J., 49 (2000), 7–30 J. Arazy and H. Upmeier, Weyl calculus for complex and real symmetric domains, In: Harmonic Analysis on Complex Homogeneous Domains and Lie Groups, Rome, 2001, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 13, 2002, pp. 165–181. J. Arazy and H. Upmeier, Invariant symbolic calculi and eigenvalues of invariant operators on symmetric domains, In: Function Spaces, Interpolation Theory and Related Topics, Lund, 2000, de Gruyter, Berlin, 2002, pp. 151–211. J. Arazy and H. Upmeier, A one-parameter calculus for symmetric domains, Math. Nachr., 280 (2007), 939–961 N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337–404 M. Atiyah and W. Schmid, A geometric construction of the discrete series of semisimple Lie groups, Invent. Math., 42 (1977), 1–62 K. Ban, On Rankin–Cohen–Ibukiyama operators for automorphic forms of several variables, Comment. Math. Univ. St. Pauli, 55 (2006), 149–171 D. Barbash, S. Sahi and B. Speh, Degenerate series representations for \(GL(2n, {\mathbb {R}})\) and Fourier analysis, In: Indecomposable Representations of Lie Groups and Their Physical Applications, Rome, 1988, (ed. V. Cantoni), Sympos. Math., 31, Academic Press, 1990, pp. 45–69. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, Ann. Physics, 111 (1978), 61–110 S. Ben Saïd, Weighted Bergman spaces on bounded symmetric domains, Pacific J. Math., 206 (2002), 39–68 F.A. Berezin, General concept of quantization, Comm. Math. Phys., 40 (1975), 153–174 F.A. Berezin, Connection between co- and contravariant symbols of operators on the classical complex symmetric spaces, Dokl. Akad. Nauk SSSR, 241 (1978), 15–17 S. Bergman, The Kernel Function and Conformal Mapping, Math. Surveys, 5, Amer. Math. Soc., 1950. W. Bertram, Un théorème de Liouville pour les algèbres de Jordan, Bull. Soc. Math. France, 124 (1996), 299–328 W. Bertram, Algebraic structures of Makarevič spaces. I, Transform. Groups, 3 (1998), 3–32 W. Bertram, The Geometry of Jordan and Lie Structures, Lecture Notes in Math., 1754, Springer-Verlag, 2000. P. Bieliavsky and M. Pevzner,Symmetric spaces and star representations. II. Causal symmetric spaces, J. Geom. Phys., 41 (2002), 224–234. P. Bieliavsky and M. Pevzner, Symmetric spaces and star representations. III. The Poincaré disc, In: Noncommutative Harmonic Analysis, Progr. Math., 220, Birkhäuser Boston, Boston, MA, 2004, pp. 61–77 P. Bieliavsky, X. Tang and Y. Yao, Rankin–Cohen brackets and formal quantization, Adv. Math., 212 (2007), 293–314 Th. Branson, Group representations arising from Lorentz conformal geometry, J. Funct. Anal., 74 (1987), 199–291 Th. Branson, G. Ólafsson and B. Órsted, Spectrum generating operators and intertwining operators for representations induced from a maximal parabolic subgroup, J. Funct. Anal., 135 (1996), 163–205 A. Cattaneo and G. Felder, A path integral approach to the Kontsevich quantization formula, Comm. Amth. Phys., 212 (2000), 591–611. A. Cattaneo and Ch. Torossian, Quantification pour les paires symetriques et diagrammes de Kontsevich, Ann. Sci. Éc. Norm. Supér. (4), to appear (2008). J.-L. Clerc, A generalized Hecke Identity, J. Fourier Anal. Appl., 6 (2000), 105–111 H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann., 217 (1975), 271–285 A. Connes and H. Moscovici, Rankin–Cohen brackets and the Hopf algebra of transverse geometry, Mosc. Math. J., 4 (2004), 111–130 G. van Dijk, A new approach to Berezin kernels and canonical representations, In: Asymptotic Combinatorics with Application to Mathematical Physics, Proceedings of the NATO Advanced Study Institute, (eds. V.A. Malyshev et al.), NATO Sci. Ser. II Math. Phys. Chem., 77, Kluwer Acad. Publ., Dordrecht, 2002, pp. 279–305. G. van Dijk and S. Hille, Canonical representations related to hyperbolic spaces, J. Funct. Anal., 147 (1997), 109–139 G. van Dijk and S. Hille, Maximal degenerate representations, Berezin kernels and canonical representations, In: Lie Groups and Lie Algebras, Math. Appl., 433, Kluwer Acad. Publ., Dordrecht, 1998, pp. 285–298. G. van Dijk and V.F. Molchanov, The Berezin form for rank one para-Hermitian symmetric spaces, J. Math. Pures Appl. (9), 77 (1998), 747–799 G. van Dijk and V.F. Molchanov, Tensor products of maximal degenerate series representations of the group,\(SL(n, {\mathbb{R}})\)), J. Math. Pures Appl. (9), 78 (1999), 99–119 G. van Dijk and M. Pevzner, Berezin kernels on tube domains, J. Funct. Anal., 181 (2001), 189–208 G. van Dijk and M. Pevzner, Matrix-valued Berezin kernels, In: Geometry and Analysis on Finite- and Infinite-dimensional Lie Groups, (eds. A. Strasburger et al.), Banach Center Publ., 55, Polish Acad. Sci. Inst. Math., Warszawa, 2002, pp. 269–288. G. van Dijk and M. Pevzner, Berezin kernels and maximal degenerate representations associated with Riemannian symmetric spaces of Hermitian type, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 292 (2002), 11–21 G. van Dijk, M. Pevzner and S. Aparicio, Invariant Hilbert subspaces of the oscillator representation, Indag. Math. (N.S.), 14 (2003), 309–318. G. van Dijk and M. Pevzner, Ring structures for holomorphic discrete series and Rankin–Cohen brackets, J. Lie Theory, 17 (2007), 283–305 G. van Dijk and M. Pevzner, H*-algebras and quantization of para-Hermitian spaces, Proc. Amer. Math. Soc., 136 (2008), 2253–2260 P.A.M. Dirac, The Principles of Quantum Mechanics, 3d ed., Oxford, at the Clarendon Press, 1947. V. Dolgushev, Covariant and equivariant formality theorems, Adv. Math., 191 (2005), 147–177 M. Duflo, Opérateurs différentiels bi-invariants sur un groupe de Lie, Ann. Sci. École Norm. Sup. (4), 10 (1977), 265–288 A. Dvorsky and S. Sahi, Explicit Hilbert spaces for certain unipotent representations. II, Invent. Math., 138 (1999), 203–224 A. Dvorsky and S. Sahi, Explicit Hilbert spaces for certain unipotent representations. III, J. Funct. Anal., 201 (2003), 430–456 W. Eholzer and T. Ibukiyama, Rankin–Cohen type differential operators for Siegel modular forms, Internat. J. Math., 9 (1998), 443–463 A. El Gradechi, The Lie theory of the Rankin–Cohen brackets and allied bi-differential operators, Adv. Math., 207 (2006), 484–531 M. Engliš, A mean value theorem on bounded symmetric domains, Proc. Amer. Math. Soc., 127 (1999), 3259–3268 J. Faraut, Intégrales de Riesz sur un espace symétrique ordonné, In: Geometry and Analysis on Finite- and Infinite-dimensional Lie Groups, Bȩdlewo, 2000, Banach Center Publ., 55, Polish Acad. Sci., Warsaw, 2002, pp. 289–308. J. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Sci. Publ., 1994. J. Faraut and G. Ólafsson, Causal semisimple symmetric spaces, the geometry and harmonic analysis, In: Semigroups in Algebra, Geometry and Analysis, (eds. K.H. Hofmann, J.D. Lawson and E.B. Vinberg), de Gruyter, Berlin, 1995. J. Faraut and M. Pevzner, Berezin kernels and analysis on Makarevich spaces, Indag. Math. (N.S.), 16 (2005), 461–486 J. Faraut and E.G.F. Thomas, Invariant Hilbert spaces of holomorphic functions, J. Lie Theory, 9 (1999), 383–402 M. Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2), 111 (1980), 253–311 I.M. Gelfand and L.A. Dikiy, A family of Hamiltonian structures connected with integrable nonlinear differential equations, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 136 (1978), 41 p. S. Gindikin, Fourier transform and Hardy spaces of \(\bar{\partial}\)-cohomology in tube domains, C. R. Acad. Sci. Paris Sér. I Math., 315 (1992), 1139–1143. P. Gordan, Invariantentheorie, Teubner, Leipzig, 1887. S. Gundelfinger, Zur der binären Formen, J. Reine Angew. Math., 100 (1886), 413–424 C.S. Herz, Bessel functions of matrix argument, Ann. of Math. (2), 61 (1955), 474–523 S. Hille, Canonical representations, Ph.D thesis, Leiden Univ., 1999. L. Hörmander, The Analysis of Linear Partial Differential Operators. III. Pseudo-differential Operators, Classics Math., Springer-Verlag, Berlin, 2007. R. Howe, On some results of Strichartz and Rallis and Schiffman, J. Funct. Anal., 32 (1979), 297–303 R. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc., 313 (1989), 539–570 R. Howe and S.T. Lee, Degenerate principal series representations of \(GL_n (\mathbb{C})\) and \(GL_n (\mathbb{R})\), J. Funct. Anal., 166 (1999), 244–309 R. Howe and E. Tan, Non-Abelian Harmonic Analysis. Applications of \({SL}(2,{\mathbb{R}})\) , Universi, Springer-Verlag, New York, 1992. R. Howe and E. Tan, Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations, Bull. Amer. Math. Soc., 28 (1993), 1–74 L.K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Transl. Math. Monogr., 6, Amer. Math. Soc., Providence, RI, 1963. H.P. Jakobsen and M. Vergne, Restrictions and expansions of holomorphic representations, J. Funct. Anal., 34 (1979), 29–53 K. Johnson, Degenerate principal series and compact groups, Math. Ann., 287 (1990), 703–718 K. Johnson, Degenerate principal series on tube type domains, Contemp. Math., 138 (1992), 175–187 S. Kaneyuki and M. Kozai, Paracomplex structures and affine symmetric spaces, Tokyo J. Math., 8 (1985), 81–98 I.L. Kantor, Non-linear groups of transformations defined by general norms of Jordan algebras, Soviet Math Dokl., 8 (1967), 176–180 M. Kashiwara and M. Vergne, On the Segal–Shale–Weil representations and harmonic polynomials, Invent. Math., 44 (1978), 1–47 M. Kashiwara and M. Vergne, The Campbell–Hausdorff formula and invariant hyperfunctions, Invent. Math., 47 (1978), 249–272 M. Kashiwara and M. Vergne, Functions on the Shilov boundary of the generalized half plane, In: Non-Commutative Harmonic Analysis, Lectures Notes in Math., 728, Springer-Verlag, 1979, pp. 136–176. A.A. Kirillov, Invariant operators over geometric quantities, In: Current Problems in Mathematics, Akad. Nauk SSSR, 16, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1980, pp. 3–29. A.A. Kirillov, Lectures on the Orbit Method, Grad. Stud. Math., 64, Amer. Math. Soc., Providence, RI, 2004. T. Kobayashi, Discrete decomposability of the restriction of \(A_{\mathfrak q}(\lambda)\) with respect to reductive subgroups and its applications, Invent. Math., 117 (1994), 181–205 T. Kobayashi, The restriction of \(A_{\mathfrak q}(\lambda)\) to reductive subgroups. I, Proc. Japan Acad. Sér. A Math. Sci., 69 (1993), 262–267; II, ibid., 71 (1995), 24–26. T. Kobayashi, Multiplicity-free theorem in branching problems of unitary highest weight modules, In: Proceedings of the Symposium on Representation Theory, Saga, Kyushu, (ed. K. Mimachi), 1997, pp. 9–17. T. Kobayashi, Discrete decomposability of the restriction of \(A_{\mathfrak q}(\lambda)\) with respect to reductive subgroups. II. Microlocal analysis and asymptotic K-support, Ann. of Math. (2), 147 (1998), 709–729 T. Kobayashi, Discrete decomposability of the restriction of \(A_{\mathfrak q}(\lambda)\) with respect to reductive subgroups. III. Restriction of Harish-Chandra modules and associated varieties, Invent. Math., 131 (1998), 229–256 T. Kobayashi, Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups, J. Funct. Anal., 152 (1998), 100–135 T. Kobayashi, Theory of discretely decomposable restrictions of unitary representations of semisimple Lie groups and some applications, Sugaku Expositions, 18 (2005), 1–37 T. Kobayashi, Multiplicity-free representations and visible actions on complex manifolds, Publ. Res. Inst. Math. Sci., 41 (2005), 497–549 T. Kobayashi, Visible actions on symmetric spaces, Transform. Groups, 12 (2007), 671–694 T. Kobayashi, Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs, In: Representation Theory and Automorphic Forms, Progr. Math., 255, Birkhäuser Boston, Boston, MA, 2007, pp. 45–109. T. Kobayashi and B. Órsted, Analysis on the minimal representation of O(p,q). I. Realization via conformal geometry, Adv. Math., 180 (2003), 486–512 T. Kobayashi and B. Órsted, Analysis on the minimal representation of O(p,q). II. Branching laws, Adv. Math., 180 (2003), 513–550 T. Kobayashi and B. Órsted, Analysis on the minimal representation of O(p,q). III. Ultrahyperbolic equations on \({\mathbb{R}}^{p-1,q-1}\), Adv. Math., 180 (2003), 551–595 M. Koecher, Über eine Gruppe von rationalen Abbildungen, Invent. Math., 3 (1967), 136–171 M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys., 66 (2003), 157–216 B. Kostant, A branching law for subgroups fixed by an involution and a noncompact analogue of the Borel–Weil theorem, In: Noncommutative Harmonic Analysis, Progr. Math., 220, Birkhäuser Boston, Boston, MA, 2004, pp. 291–353. B. Kostant and S. Sahi, The Capelli identity, tube domains, and the generalized Laplace transform, Adv. Math., 87 (1991), 71–92 B. Kostant and S. Sahi, Jordan algebras and Capelli identities, Invent. Math., 112 (1993), 657–664 B. Krötz, On Hardy and Bergman spaces on complex Ol’shanskiǐ semigroups, Math. Ann., 312 (1998), 13–52 P.D. Lax and R.S. Phillips, Scattering Theory for Automorphic Functions, Ann. of Math. Stud., 87, Princeton Univ. Press, 1976. S. Lee, On some degenerate principal series representations of U(n,n), J. Funct. Anal., 126 (1994), 305–366 S. Lee, Degenerate principal series representations of \(Sp(2n, {\mathbb{R}})\) , Compositio Math., 103 (1996), 123–151 J. Liouville, Théorème sur l’équation \(dx^2+dy^2+dz^2=\lambda(d\alpha^2+d\beta^2+d\gamma^2)\) , J. Math. Pures Appl., 15 (1850), p. 103 O. Loos, Symmetric Spaces. I, II, Benjamin, New York, 1969. G.W. Mackey, Unitary Group Representations in Physics, Probability and Number Theory, Math. Lecture Note Ser., 55, Benjamin/Cummings Publ. Co., Inc., Reading, Mass., 1978; Second ed., Adv. Book Classics, Addison-Wesley Publ. Co., Rewood City, CA, 1989. D. Manchon and Ch. Torossian, Cohomologie tangente et cup-produit pour la quantification de Kontsevich, Ann. Math. Blaise Pascal, 10 (2003), 75–106 V.F. Molchanov, Tensor products of unitary representations of the three-dimensional Lorentz group, Math. USSR-Izv., 15 (1980), 113–143 V.F. Molchanov, Maximal degenerate series representations of the universal covering of the group SU(n,n), In: Lie Groups and Lie Algebras. Their Representations, Generalisations and Applications, (eds. B.P. Komrakov et al.), Math. Appl., 433, Kluwer Acad. Publ., 1998, pp. 313–336 Yu. Neretin, Matrix analogues of the B-function, and the Plancherel formula for Berezin kernel representations, Sb. Math., 191 (2000), 683–715 Yu. Neretin, Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants, Mosc. Math. J., 1 (2001), 157–220 Yu. Neretin, (2002) Plancherel formula for Berezin deformation of L 2 on Riemannian symmetric space, J. Funct. Anal., 189 336–408 T. Nomura, Berezin transforms and group representations, J. Lie Theory, 8 (1998), 433–440 G. Ólafsson and B. Órsted, The holomorphic discrete series for affine symmetric spaces. I, J. Funct. Anal., 81 (1988), 126–159 G.I. Olshanski, Invariant cones in Lie algebras, Lie semigroups and holomorphic discrete series, Funct. Anal. Appl., 15 (1981), 275–285 P.J. Olver, Classical Invariant Theory, London Math. Soc. Stud. Texts, 44, Cambridge Univ. Press, 1999. P.J. Olver and J.A. Sanders, Transvectants, modular forms, and the Heisenberg algebra, Adv. in Appl. Math., 25 (2000), 252–283 B. Órsted and B. Speh, Branching laws for some unitary representations of SL(4,\({\mathbb{R}}\)), SIGMA Symmetry Integrability Geom. Methods Appl., 4 (2008), 19 p. B. Órsted and J. Vargas, Restriction of square integrable representations: discrete spectrum, Duke Math. J., 123, (2004) 609–633 B. Órsted and G. Zhang, Generalized principal series representations and tube domains, Duke Math. J., 78 (1995), 335–357 B. Órsted and G. Zhang, Capelli identity and relative discrete series of line bundles over tube domains, In: Geometry and Analysis on Finite- and Infinite-dimensional Lie Groups, Proceedings of the workshop on Lie groups and Lie algebras, Bedlewo, Poland, September 4-15, 2000,Banach Center Publ., 55, Polish Acad. Sci., Warszawa, 2002, pp. 349–357 T. Oshima and T. Matsuki, A description of discrete series for semisimple symmetric spaces, In: Group Representations and Systems of Differential Equations, Adv. Stud. Pure Math., 4, 1984, pp. 331–390 T. Oshima and T. Matsuki, A description of discrete series for semisimple symmetric spaces, In: Group Representations and Systems of Differential Equations, Adv. Stud. Pure Math., 4, 1984, pp. 331–390 E. Pedon, Harmonic analysis for differential forms on complex hyperbolic spaces, J. Geom. Phys., 32 (1999), 102–130 J. Peetre, Hankel forms of arbitrary weight over a symmetric domain via the transvectant, Rocky Mountain J. Math., 24 (1994), 1065–1085 L. Peng, and G. Zhang, Tensor products of holomorphic representations and bilinear differential operators, J. Funct. Anal., 210 (2004), 171–192 M. Pevzner, Espace de Bergman d’un semi-groupe complexe, C. R. Acad. Sci. Paris Sér. I Math., 322(1996), 635–640 M. Pevzner, Analyse conforme sur les algèbres de Jordan, Ph.D. thesis, Univ. of Paris VI, 1998. M. Pevzner, Représentation de Weil associée à une représentation d’une algèbre de Jordan, C. R. Acad. Sci. Paris Sér. I Math., 328 (1999), 463–468 M. Pevzner, Analyse conforme sur les algèbres de Jordan, J. Aust. Math. Soc., 73 (2002), 279–299 M. Pevzner and Ch. Torossian, Isomorphisme de Duflo et la cohomologie tangentielle, J. Geom. Phys., 51 (2004), 486–505. M. Pevzner and A. Unterberger, Projective pseudodifferential analysis and harmonic analysis, J. Funct. Anal., 242 (2007), 442–485 M. Pevzner, Rankin–Cohen brackets and associativity, Lett. Math. Phys., 85 (2008), 195–202 J. Repka, Tensor products of holomorphic discrete series representations, Canad. J. Math., 31 (1979), 836–844 F. Rouvière, Invariant analysis and contractions of symmetric spaces. I, Compositio Math., 73 (1990), 241–270; II, Compositio Math., 80 (1991), 11–136. F. Rouvière, Fibrés en droites sur un espace symétrique et analyse invariante, J. Funct. Anal., 124 (1994), 263–291 H. Rubenthaler, Une série dégénérée de représentations de \(SL_n({\mathbb{R}})\), Lecture Notes in Math., 739 (1979), 427–459 S. Sahi, The Capelli identity and unitary representations, Compositio Math., 81 (1992), 247–260 S. Sahi, Explicit Hilbert spaces for certain unipotent representations, Invent. Math., 110 (1992), 409–418 S. Sahi, Unitary representations on the Shilov boundary of a symmetric tube domain, In: Representation Theory of Groups and Algebras, Contemp. Math., 145, Amer. Math. Soc., Providence, RI, 1993, pp. 275–286. S. Sahi, Jordan algebras and degenerate principal series, J. Reine Angew. Math., 462 (1995), 1–18 S. Sahi and E.M. Stein, Analysis in matrix space and Speh’s representations, Invent. Math., 101 (1990), 379–393 I. Satake, Algebraic Structures of Symmetric Domains, Iwanami Shoten; Princeton Univ. Press, 1980. M. Schlichenmaier, Berezin–Toeplitz quantization and Berezin transform, In: Long Time Behaviour of Classical and Quantum Systems, Proceedings of the Bologna APTEX international conference, Bologna, (ed. S. Graffi), Ser. Concr. Appl. Math., 1, World Sci. Publ., Singapore, 2001, pp. 271–287. W. Schmid, Construction and classification of irreducible Harish-Chandra modules, In: Harmonic Analysis on Reductive Groups, Brunswick, ME, 1989, Progr. Math., 101, Birkhäuser Boston, Boston, MA, 1991, pp. 235–275. L. Schwartz, Sous-espaces hilbertiens d’espaces vectoriels topologiques et noyaux associés, J. Analyse Math., 13 (1964), 115–256 H. Seppänen, Branching laws for minimal holomorphic representations, J. Funct. Anal., 251 (2007), 174–209 B. Shoikhet, On the Duflo formula for L ∞-algebras and Q-manifolds, e-print, QA/9812009. M.A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, 2001. R.S. Strichartz, Harmonic analysis on hyperboloids, J. Functional Analysis, 12 (1973), 341–383 E.G.F. Thomas, The theorem of Bochner–Schwartz–Godement for generalised Gelfand pairs, In: Functional Analysis: Surveys and Recent Results. III, Paderborn, 1983, North-Holland Math. Stud., 90, 1984, pp. 291–304. E.G.F. Thomas, Integral representations in conuclear cones, J. Convex Anal., 1 (1994), 225–258 P. Torasso, Méthode des orbites de Kirillov–Duflo et représentations minimales des groupes simples sur un corps local de caractéristique nulle,Duke Math. J., 90 (1997), 261–377 Ch. Torossian, Opérateurs différentiels invariants sur les espaces symétriques. I. Méthodes des orbites, J. Funct. Anal., 117 (1993), 118–173 Ch. Torossian, Opérateurs différentiels invariants sur les espaces symétriques. II. L’homomorphisme de Harish-Chandra généralisé, J. Funct. Anal., 117 (1993), 174–214 Ch. Torossian, Sur la conjecture combinatoire de Kashiwara–Vergne, J. Lie Theory, 12 (2002), 597–616 Ch. Torossian, Méthodes de Kashiwara–Verge–Rouvière pour les espaces symétriques, In: Noncommutative Harmonic Analysis, Progr. Math., 220, Birkhäuser Boston, Boston, MA, 2004, pp. 459–486. F. Trèves, Introduction to Pseudodifferential and Fourier Integral Operators. Vol. 1, Pseudodifferential operators, The University Series in Mathematics, Plenum Press, New York-London, 1980. A. Unterberger, Quantization and Non-holomorphic Modular Forms, Lecture Notes in Math., 1742, Springer-Verlag, Berlin, 2000. A. Unterberger and J. Unterberger, La série discrète de \({\rm SL}(2, {\mathbb {R}})\) et les opérateurs pseudo-différentiels sur une demi-droite, Ann. Sci. École Norm. Sup. (4), 17 (1984), 83–116 A. Unterberger and J. Unterberger, Quantification et analyse pseudo-différentielle, Ann. Sci. École Norm. Sup. (4), 21 (1988), 133–158 A. Unterberger and J. Unterberger, Algebras of symbols and modular forms, J. Anal. Math., 68 (1996), 121–143 A. Unterberger and H. Upmeier, The Berezin transform and invariant differential operators, Comm. Math. Phys., 164 (1994), 563–597 A.M. Vershik, I.M. Gelfand and M.I. Graev, Representations of the group SL(2, R), where R is a ring of functions, Uspehi Mat. Nauk, 28 (1973), 83–128 E.B. Vinberg, Invariant convex cones and orderings in Lie groups, Funct. Anal. Appl., 14 (1980), 1–13 A. Weil, Sur certains groupes d’opérateurs unitaires, Acta Math., 111 (1964), 143–211 H. Weyl, Gruppentheorie und Quantenmechanik, 2nd ed., S. Hirzel Verlag, Leipzig, 1931. D. Zagier, Introduction to modular forms, In: From Number Theory to Physics, (eds. W. Waldschmidt, P. Moussa, J.-M. Luck and C. Itzykson), Springer-Verlag, Berlin, 1992, pp. 238–291. D. Zagier, Modular forms and differential operators, Proc. Indian Acad. Sci. Math. Sci., 104 (1994), 57–75 G. Zhang, Jordan algebras and generalized principal series representations, Math. Ann., 302 (1995), 773–786 G. Zhang, Berezin transform on compact Hermitian symmetric spaces, Manuscripta Math., 97 (1998), 371–388 G. Zhang, Berezin transform on real bounded symmetric domains, Trans. Amer. Math. Soc., 353 (2001), 3769–3787 G. Zhang, Branching coefficients of holomorphic representations and Segal–Bargmann transform, J. Funct. Anal., 195 (2002), 306–349