Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908337043406848 |
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| author | Teyssier, Lucas Thévenin, Paul |
| author_facet | Teyssier, Lucas Thévenin, Paul |
| contents | We prove sharp bounds on the virtual degrees introduced by Larsen and Shalev. This leads to improved bounds on characters of symmetric groups. We then sharpen bounds of Liebeck and Shalev concerning the Witten zeta function. Our main application is a characterization of the fixed-point free conjugacy classes whose associated random walk mixes in 2 steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function Teyssier, Lucas Thévenin, Paul Representation Theory Combinatorics Probability 20C30, 60J10, 05E10 We prove sharp bounds on the virtual degrees introduced by Larsen and Shalev. This leads to improved bounds on characters of symmetric groups. We then sharpen bounds of Liebeck and Shalev concerning the Witten zeta function. Our main application is a characterization of the fixed-point free conjugacy classes whose associated random walk mixes in 2 steps. |
| title | Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function |
| topic | Representation Theory Combinatorics Probability 20C30, 60J10, 05E10 |
| url | https://arxiv.org/abs/2411.04347 |