Restriction of Representations of GL (n + 1, ℂ) to GL (n, ℂ) and Action of the Lie Overalgebra

Anh, N.H.: Restriction of the principal series of S L(n,C) to some reductive subgroups. Pac. J. Math. 38, 295–314 (1971)

Asherova, R.M., Smirnov, Yu. F., Tolstoi, B.N.: Projection operators for simple lie groups II. General scheme for constructing lowering operators. The groups S U(n). Theor. Math. Phys. 15(1), 392–401 (1973)

Baird, G.E., Biedenharn, L.C.: On the Representations of the Semisimple Lie Groups. II. J. Math. Phys. 4(1449), 1449–1466 (1963)

Fulton, W.: Young tableaux With applications to representation theory and geometry. Cambridge University Press, Cambridge (1997)

Gelfand, I.M., Graev, M.I.: Finite-dimensional irreducible representations of the unitary and complete linear group and special functions associated with them. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 29, 1329–1356 (1965). English transl. in Amer. Math. Soc. Transl. Series 2 64 (1965), 116-146

Gelfand, I.M., Naimark, M.A.: Unitary representations of the classical groups. Trudy Mat. Inst. Steklov., vol. 36, Izdat. Akad. Nauk SSSR, Moscow-Leningrad, 1950. German transl.: Gelfand, I. M.; Neumark, M. A., Unitäre Darstellungen der klassischen Gruppen. Akademie-Verlag, Berlin (1957)

Gelfand, I.M., Tsetlin, M.L.: Finite-dimensional representations of the group of unimodular matrices. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 71, 825–828 (1950). English transl. in I. M. Gelfand, Collected Papers, Vol. II, Springer, Berlin, 1988, 653–656

Gelfand, I.M., Tsetlin, M.L.: Finite-dimensional representations of groups of orthogonal matrices. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 71, 1017–1020 (1950). English transl. I. M. Gelfand, Collected Papers, Vol. II, Springer, Berlin, 1988, 657–661

Graev, M.I.: A continuous analogue of Gelfand-Tsetlin schemes and a realization of the principal series of irreducible unitary representations of the group G L ( n , ℂ ) $\mathrm {G}\mathrm {L}(n,\mathbb {C})$ in the space of functions on the manifold of these schemes. Dokl. Math. 75(1), 31–35 (2007)

Groenevelt, W.: The Wilson function transform. Int. Math. Res. Not. 52, 2779–2817 (2003)

Mickelsson, J.: Step algebras of semi-simple subalgebras of Lie algebras. Rep. Math. Phys. 4, 307–318 (1973)

Molchanov, V.F.: Canonical representations and overgroups for hyperboloids of one sheet and Lobachevsky spaces. Acta Appl. Math. 86(1-2), 115–129 (2005)

Molchanov, V.F.: Canonical representations and overgroups for hyperboloids. Funct. Anal. Appl. 4, 284–295 (2005)

Molchanov, V.F.: Canonical representations on Lobachevsky spaces: an interaction with an overalgebra. Acta Appl. Math. 99(3), 321–337 (2007)

Molchanov, V.F.: Poisson transforms for tensor products. Funct. Anal Fourier Appl. 4, 279–288 (2015)

Molev, A.I.: Unitarizability of some Enright-Varadarajan u(p, q)-modules. In: Topics in representation theory, 199-219, Advance in Soviet Mathematics, vol. 2. American Mathematical Society, Providence (1991)

Molev, A.I.: A basis for representations of symplectic Lie algebras. Comm. Math. Phys. 201(3), 591–618 (1999)

Molev, A.: Yangians and classical Lie algebras. American Mathematical Society, Providence (2007)

Nazarov, M.A., Tarasov, V.: Yangians and Gelfand-Zetlin bases. Publ. Res. Inst. Math. Sci. 30(3), 459–478 (1994)

Neretin, Yu.A.: The action of an overalgebra in the Plancherel decomposition and shift operators in an imaginary direction. Izv. Math. 66(5), 1035–1046 (2002)

Neretin, Yu.A.: Notes on Stein-Sahi representations and some problems of non-L 2-harmonic analysis. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 331, 14,125–169,224 (2006). translation in J. Math. Sci. (N. Y.) 141 (2007), no. 4, 14521478

Neretin, Yu.A.: Lectures on Gaussian integral operators and classical groups. European Mathematical Society (2011)

Neretin, Yu.A.: Difference Sturm-Liouville problems in the imaginary direction. J. Spectr. Theory 3(3), 237–269 (2013)

Neretin, Yu.A.: Hua-Type Beta-Integrals and Projective Systems of Measures on Flag Spaces. IMRN, v. 21, 11289–11301 (2015)

Neretin, Yu.A.: The Fourier transform on the group G L 2 ( ℝ ) $\mathrm {G}\mathrm {L}_{2}(\mathbb {R})$ and the action of the overalgebra 𝔤 𝔩 4 $\mathfrak {gl}_{4}$ . J. Fourier Analysis, https://doi.org/10.1007/s00041-017-9589-8

Neretin, Yu.A.: Operational calculus for Fourier transform on the group GL ( 2 , ℝ ) $GL(2,\mathbb {R})$ . arXiv: 1801.09398

Olshanski, G.I.: Description of unitary representations with highest weight for the groups U ( p , q ) ∼ $\mathrm {U}(p,q)^{\sim }$ . Funct. Anal. Appl. 14(3), 190–200 (1981)

Shtepin, V.V.: Intermediate Lie algebras and their finite-dimensional representations. Russian Acad. Sci. Izv. Math. 43(3), 559-579 (1994)

Zhelobenko, D.P.: Classical groups. Spectral analysis of finite-dimensional representations. Russ. Math. Surveys 17(1), 1–94 (1962)

Zhelobenko, D.P.: Compact Lie groups and their representations. American Mathematical Society, Providence (1973)

Zhelobenko, D.P.: Representations of reductive Lie algebras. (Russian) VO “Nauka”, Moscow (1994)

Zhelobenko, D.: Principal structures and methods of representation theory. American Mathematical Society, Providence (2006)