Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras
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 $\mathfrak{S}_n$ are given by plethystically transformed Macdonald polynomials specialized at q=t. We generalize this to restricted rational Cherednik algebras of wreath product groups $C_\ell \wr \mathfrak{S}_n$ and prove that the corresponding characters are given by a specialization of the wreath Macdonald polynomials defined by Haiman.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 DOI:
 10.48550/arXiv.2112.10604
 arXiv:
 arXiv:2112.10604
 Bibcode:
 2021arXiv211210604M
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Combinatorics