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Mathematics > Quantum Algebra

arXiv:0709.1742 (math)
[Submitted on 12 Sep 2007 (v1), last revised 1 Nov 2008 (this version, v4)]

Title:Non-semisimple Macdonald polynomials

Authors:Ivan Cherednik
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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.
Comments: 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
Subjects: Quantum Algebra (math.QA); Representation Theory (math.RT)
Cite as: arXiv:0709.1742 [math.QA]
  (or arXiv:0709.1742v4 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.0709.1742

Submission history

From: Ivan Cherednik [view email]
[v1] Wed, 12 Sep 2007 01:59:08 UTC (142 KB)
[v2] Thu, 18 Oct 2007 22:45:38 UTC (144 KB)
[v3] Sun, 4 Nov 2007 18:01:05 UTC (147 KB)
[v4] Sat, 1 Nov 2008 20:53:44 UTC (152 KB)
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