| Autor: |
Cheng Shu |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
Forum of Mathematics, Sigma, Vol 11 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2050-5094 |
| DOI: |
10.1017/fms.2023.119 |
| Popis: |
For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\operatorname {\mathrm {GL}}_n\rtimes \!}$ -character varieties. We restrict the monodromies around the branch points to generic semi-simple conjugacy classes contained in $\operatorname {\mathrm {GL}}_n\sigma $ and compute the E-polynomials of these character varieties using the character table of $\operatorname {\mathrm {GL}}_n(q)\rtimes \!\!$ . The result is expressed as the inner product of certain symmetric functions associated to the wreath product $(\mathbb {Z}/2\mathbb {Z})^N\rtimes \mathfrak {S}_N$ . We are then led to a conjectural formula for the mixed Hodge polynomial, which involves (modified) Macdonald polynomials and wreath Macdonald polynomials. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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