Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras

2021/12/20 by Dario Mathiä, Mathiä, Dario, Ulrich Thiel +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2112.10604

openalex publication_date 2021/12/20 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Using the theory of Macdonald, Gordon showed that the graded characters of the simple modules for the restricted rational Cherednik algebra by Etingof and Ginzburg associated to the symmetric group \mathfrakS_n are given by plethystically transformed Macdonald polynomials specialized at q=t. We generalize this to restricted rational Cherednik algebras of wreath product groups C_ℓ \wr \mathfrakS_n and prove that the corresponding characters are given by a specialization of the wreath Macdonald polynomials defined by Haiman.

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