Reflection groups in analysis and applications

C. Abdelkefi and M. Sifi, Characterization of Besov spaces for the Dunkl operator on the real line, JIPAM. J. Inequal. Pure Appl. Math., 8 (2007), no. 3, article 73, 11 p.

T.H. Baker and P.J. Forrester, The Calogero–Sutherland model and generalized classical polynomials, Comm. Math. Phys., 188 (1997), 175–216

J.J. Betancor, Distributional Dunkl transform and Dunkl convolution operators, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 9 (2006), 221–245

H.S.M. Coxeter, Regular Polytopes, 3rd ed., Dover Press, New York, 1973.

N. Crampé and C.A.S. Young, Sutherland models for complex reflection groups, Nuclear Phys. B, 797 (2008), 499–519, arXiv:0708.2664v2, 29 Nov. 2007

F. Dai and Y. Xu, Cesàro means of orthogonal expansions in several variables, Constr. Approx., to appear, arXiv:0705.2477v1, 17 May 2007.

C.F. Dunkl, A Krawtchouk polynomial addition theorem and wreath products of symmetric groups, Indiana Univ. Math. J., 25 (1976), 335–358

C.F. Dunkl, An addition theorem for Hahn polynomials: the spherical functions, SIAM J. Math. Anal., 9 (1978), 627–637

C.F. Dunkl, Orthogonal polynomials on the sphere with octahedral symmetry, Trans. Amer. Math. Soc., 282 (1984), 555–575

C.F. Dunkl, Reflection groups and orthogonal polynomials on the sphere, Math. Z., 197 (1988), 33–60

C.F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc., 311 (1989), 167–183

C.F. Dunkl, Poisson and Cauchy kernels for orthogonal polynomials with dihedral symmetry, J. Math. Anal. Appl., 143 (1989), 459–470

C.F. Dunkl, Operators commuting with Coxeter group actions on polynomials, Invariant Theory and Tableaux, (ed. D. Stanton), IMA Vol. Math. Appl., 19, Springer-Verlag, 1990, pp. 107–117.

C.F. Dunkl, Integral kernels with reflection group invariance, Canad. J. Math., 43 (1991), 1213–1227

C.F.Dunkl, Hankel transforms associated to finite reflection groups, Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, Contemp. Math., 138, Amer. Math. Soc., Providence, RI, 1992, pp. 123–138.

C.F. Dunkl, Intertwining operators associated to the group S 3, Trans. Amer. Math. Soc., 347 (1995), 3347–3374

C.F. Dunkl, Orthogonal polynomials of types A and B and related Calogero models, Comm. Math. Phys., 197 (1998), 451–487

C.F. Dunkl, Singular polynomials for the symmetric groups, Int. Math. Res. Not., 2004 (2004), 3607–3635

C.F. Dunkl, Singular polynomials and modules for the symmetric groups, Int. Math. Res. Not., 2005 (2005), 2409–2436

C.F. Dunkl, An intertwining operator for the group B 2, Glas. Math. J., 49 (2007), 291–319

C.F. Dunkl, M.F.E. de Jeu and E.M. Opdam, Singular polynomials for finite reflection groups, Trans. Amer. Math. Soc., 346 (1994), 237–256

C.F. Dunkl and E.M. Opdam, Dunkl operators for complex reflection groups, Proc. London Math. Soc. (3), 86 (2003), 70–108

C.F. Dunkl and Y. Xu, Orthogonal Polynomials of Several Variables, Encyclopedia Math. Appl., 81, Cambridge Univ. Press, Cambridge, 2001

P. Etingof and X. Ma, On elliptic Dunkl operators, arXiv:0706.2152v1, 14 Jun. 2007.

P.J. Forrester, D.S. McAnally and Y. Nikoyalevsky, On the evaluation formula for Jack polynomials with prescribed symmetry, J. Phys. A, 34 (2001), 8407–8424

L. Gallardo and M. Yor, A chaotic representation property of the multidimensional Dunkl processes, Ann. Probab., 34 (2006), 1530–1549

V. Ginzburg, N. Guay, E.M. Opdam and R. Rouquier, On the category $${\fancyscript{O}}$$ for rational Cherednik algebras, Invent. Math., 154 (2003), 617–651.

S. Griffeth, On some orthogonal functions generalizing Jack polynomials, arXiv:0707.0251v2, 20 May 2008.

G.J. Heckman, A remark on the Dunkl differential-difference operators, Harmonic Analysis on Reductive Groups, Brunswick, ME, 1989, Progr. Math., 101, Birkhäuser Boston, Boston, MA, 1991, pp. 181–191.

K. Hikami, Dunkl operator formalism for quantum many-body problems associated with classical root systems, J. Phys. Soc. Japan, 65 (1996), 394–401

K. Hikami and M. Wadati, Topics in quantum integrable systems, integrability, topological solitons and beyond, J. Math. Phys., 44 (2003), 3569–3594

J.E. Humphreys, Reflection groups and Coxeter groups, Cambridge Stud. Adv. Math., 29, Cambridge Univ. Press, Cambridge, 1990

M.F.E. de Jeu, The Dunkl transform, Invent. Math., 113 (1993), 147–162

F. Knop and S. Sahi, A recursion and a combinatorial formula for Jack polynomials, Invent. Math., 128 (1997), 9–22

T.H. Koornwinder, Yet another proof of the addition formula for Jacobi polynomials, J. Math. Anal. Appl., 61 (1977), 136–141

S. Lawi, Towards a characterization of Markov processes enjoying the time-inversion property, J. Theoret. Probab., 21 (2008), 144–168

I.G. Macdonald, Affine Hecke algebras and Orthogonal Polynomials, Cambridge Tracts in Math., 157, Cambridge Univ. Press, Cambridge, 2003.

M. Maslouhi and E.H. Youssfi, Harmonic functions associated to Dunkl operators, Monatsh. Math., 152 (2007), 337–345

M.A. Mourou, Transmutation operators associated with a Dunkl-type differential-difference operator on the real line and certain of their applications, Integral Transform. Spec. Funct., 12 (2001), 77–88

G.E. Murphy, A new construction of Young’s seminormal representation of the symmetric groups, J. Algebra, 69 (1981), 287–297

S. Odake and R. Sasaki, Exact Heisenberg operator solutions for multiparticle quantum mechanics, J. Math. Phys., 48 (2007), no. 8, 082106, 12 p., arXiv:0706.0768v1, 6 Jun. 2007.

E.M. Opdam, Dunkl operators, Besse functions and the discriminant of a finite Coxeter group, Compositio Math., 85 (1993), 333–373

E.M. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math., 175 (1995), 75–121

E.M. Opdam, Lecture Notes on Dunkl Operators for Real and Complex Reflection Groups, (with a preface by T. Oshima), MSJ Mem., 8, Math. Soc. Japan, Tokyo, 2000.

M. Rösler, Positivity of Dunkl’s intertwining operator, Duke Math. J., 98 (1999), 445–463

M. Rösler and M. de Jeu, Asymptotic analysis for the Dunkl kernel, J. Approx. Theory, 119 (2002), 110–126

M. Rösler and M. Voit, Markov processes related with Dunkl operators, Adv. in Appl. Math., 21 (1998), 575–643

R. Rouquier, Representations of rational Cherednik algebras, Infinite-Dimensional Aspects of Representation Theory and Applications, Contemp. Math., 392, Amer. Math. Soc., Providence, RI, 2005, pp. 103–131.

S. Thangavelu and Y. Xu, Convolution operator and maximal function for the Dunkl transform, J. Anal. Math., 97 (2005), 25–55

K. Trimèche, The Dunkl intertwining operator on spaces of functions and distributions and integral representation of its dual, Integral Transform. Spec. Funct., 12 (2001), 349–374

H. Ujino and M. Wadati, Rodrigues formula for Hi-Jack symmetric polynomials associated with the quantum Calogero model, J. Phys. Soc. Japan, 65 (1996), 2423–2439

H. Volkmer, Generalized ellipsoidal and sphero-conal harmonics, SIGMA Symmetry Integrability Geom. Methods Appl., 2 (2006), paper 071, 16 p.