Affine Hecke Algebras and Orthogonal Polynomials

Introduction 1. Affine root systems 2. The extended affine Weyl group 3. The braid group 4. The affine Hecke algebra 5. Orthogonal polynomials 6. The rank 1 case Bibliography Index.

[1]  Mizan Rahman,et al.  Basic Hypergeometric Series , 1990 .

[2]  E. Opdam.  Harmonic analysis for certain representations of graded Hecke algebras , 1995 .

[3]  Eric M. Opdam,et al.  Some applications of hypergeometric shift operators , 1989 .

[4]  Alexander Kirillov,et al.  Lectures on affine Hecke algebras and Macdonald’s conjectures , 1997 .

[5]  E. Opdam,et al.  Root systems and hypergeometric functions. I , 1988 .

[6]  Egbert Brieskorn,et al.  Artin-Gruppen und Coxeter-Gruppen , 1972 .

[7]  Ivan Cherednik,et al.  Double affine hecke algebras, knizhnik-zamolodchikov equations, and macdonald’s operators , 1992 .

[8]  Robert V. Moody,et al.  Euclidean Lie Algebras , 1969, Canadian Journal of Mathematics.

[9]  R. A. Gustafson,et al.  A generalization of Selberg’s beta integral , 1990 .

[10]  Orthogonal polynomials associated with root systems , 2000, math/0011046.

[11]  L. J. Rogers.  On the Expansion of some Infinite Products , 1892 .

[12]  B. Ion.  Involutions of Double Affine Hecke Algebras , 2001, Compositio Mathematica.

[13]  I. G. MacDonald,et al.  Affine root systems and Dedekind'sη-function , 1971 .

[14]  I. Macdonald.  The Poincaré series of a Coxeter group , 1972 .

[15]  Ivan Cherednik,et al.  Nonsymmetric Macdonald polynomials , 1995 .

[16]  F. Dyson.  Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[17]  I. G. MacDonald,et al.  Spherical functions on a group of p-adic type , 1971 .

[18]  Nonsymmetric Koornwinder polynomials and duality , 1997, q-alg/9710032.

[19]  I. Cherednik.  Intertwining operators of double affine Hecke algebras , 1996, q-alg/9605014.

[20]  R. Moody.  A new class of Lie algebras , 1968 .

[21]  I. Cherednik.  Macdonald’s evaluation conjectures and difference Fourier transform , 1995, q-alg/9503006.

[22]  Self-dual Koornwinder-Macdonald polynomials , 1995, q-alg/9507033.

[23]  Jacques Tits,et al.  Groupes réductifs sur un corps local , 1972 .

[24]  L. J. Rogers.  Second Memoir on the Expansion of certain Infinite Products , 1893 .

[25]  Macdonald's evaluation conjectures and difference Fourier transform , 1994, q-alg/9412016.

[26]  Tom H. Koornwinder,et al.  Askey-Wilson polynomials for root systems of type BC , 1991 .

[27]  I. G. MacDonald,et al.  Symmetric Functions and Orthogonal Polynomials , 1998 .

[28]  I. G. MacDonald,et al.  Symmetric functions and Hall polynomials , 1979 .

[29]  George Lusztig,et al.  Affine Hecke algebras and their graded version , 1989 .

[30]  I. Cherednik.  Double affine Hecke algebras and Macdonald's conjectures , 1995 .

[31]  V. Kac.  Infinite dimensional Lie algebras: Frontmatter , 1990 .

[32]  R. Askey,et al.  Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials , 1985 .

[33]  Koornwinder polynomials and affine Hecke algebras , 2000, math/0002090.

[34]  I. G. MacDonald,et al.  Some Conjectures for Root Systems , 1982 .

[35]  R. Stanley.  Some combinatorial properties of Jack symmetric functions , 1989 .

[36]  H. van der Lek,et al.  The homotopy type of complex hyperplane complements , 1983 .

[37]  George E. Andrews,et al.  Problems and Prospects for Basic Hypergeometric Functions , 1975 .