Non-semisimple Macdonald polynomials

2007/09/12 by Ivan Cherednik, Cherednik, Ivan · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0709.1742

openalex publication_date 2007/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Differential-difference operators associated to reflection groups

Cited by

• A new take on spherical, Whittaker and Bessel functions (Spherical and Whittaker functions via DAHA I,II)
• Unitary representations of rational Cherednik algebras

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