Intertwining Operators of Double Affine Hecke Algebras

Details Intertwining Operators of Double Affine Hecke Algebras Intertwining Operators of Double Affine Hecke Algebras

1996-05-09

arxiv.org/abs/q-alg/9605014v5

Mathematics

Quantum Algebra

AMSTeX, 36pg

Scientific paper

A systematic study of the representation theory of double affine Hecke algebras and related harmonic analysis is started in this paper. Continuing the previous papers we use the technique of intertwining operators to create Macdonald polynomials, estimate their denominators, generalize the classical representations of p-adic affine Hecke algebras in the spaces of functions on affine Weyl groups, and to find out when induced representations are irreducible and co-spherical. The connection with recent results by Sahi and Knop on the integrality of the Macdonald polynomials is established.

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