Non-semisimple Macdonald polynomials
Abstract
Description
The paper is mainly devoted to the irreducibility of the polynomial representation of the double affine Hecke algebra for an arbitrary reduced root systems and generic "central charge" q. The technique of intertwiners in the non-semisimple variant is the main tool. We introduce Macdonald's non-semisimple polynomials and use them to analyze the reducibility of the polynomial representation in terms of the affine exponents, counterparts of the classical Coxeter exponents. The focus is on the principal aspects of the technique of intertwiners, including related problems in the theory of reduced decompositions on affine Weyl groups.
The changes vs. the first variant: a) minor corrections and improvements, b) the q-q'-duality for the affine exponents was added, c) the connectionwith the classical Poincare polynomial is more explicit now, d) the case when t are roots of unity (generic q) was incorporated; v4: to be published by Selecta Math.: editing, better references
The changes vs. the first variant: a) minor corrections and improvements, b) the q-q'-duality for the affine exponents was added, c) the connectionwith the classical Poincare polynomial is more explicit now, d) the case when t are roots of unity (generic q) was incorporated; v4: to be published by Selecta Math.: editing, better references