Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866917261152878592 |
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| author | Mathiä, Dario Thiel, Ulrich |
| author_facet | Mathiä, Dario Thiel, Ulrich |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_10604 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras Mathiä, Dario Thiel, Ulrich Representation Theory Combinatorics 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. |
| title | Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2112.10604 |