Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context.

This is an essentially self-contained monograph centered on the new double Hecke algebra technique.

First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.

Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had s

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited pape