Character bounds for finite groups of Lie type
We establish new bounds on character values and character ratios for finite groups G of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form |χ(g)|⩽cχ(1)αg, and give rise to a variety of applications, for exampl...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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International Press of Boston
2021
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| Online Access: | https://hdl.handle.net/1721.1/122808.2 |
| _version_ | 1811082467604430848 |
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| author | Bezrukavnikov, Roman Liebeck, Martin W. Shalev, Aner Tiep, Pham Huu |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman Liebeck, Martin W. Shalev, Aner Tiep, Pham Huu |
| author_sort | Bezrukavnikov, Roman |
| collection | MIT |
| description | We establish new bounds on character values and character ratios for finite groups G of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form |χ(g)|⩽cχ(1)αg, and give rise to a variety of applications, for example to covering numbers and mixing times of random walks on such groups. In particular, we deduce that, if G is a classical group in dimension n, then, under some conditions on G and g∈G, the mixing time of the random walk on G with the conjugacy class of g as a generating set is (up to a small multiplicative constant) n/s, where s is the support of g. |
| first_indexed | 2024-09-23T12:03:53Z |
| format | Article |
| id | mit-1721.1/122808.2 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:03:53Z |
| publishDate | 2021 |
| publisher | International Press of Boston |
| record_format | dspace |
| spelling | mit-1721.1/122808.22021-09-07T17:53:17Z Character bounds for finite groups of Lie type Bezrukavnikov, Roman Liebeck, Martin W. Shalev, Aner Tiep, Pham Huu Massachusetts Institute of Technology. Department of Mathematics We establish new bounds on character values and character ratios for finite groups G of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form |χ(g)|⩽cχ(1)αg, and give rise to a variety of applications, for example to covering numbers and mixing times of random walks on such groups. In particular, we deduce that, if G is a classical group in dimension n, then, under some conditions on G and g∈G, the mixing time of the random walk on G with the conjugacy class of g as a generating set is (up to a small multiplicative constant) n/s, where s is the support of g. NSF (Grants DMS-1102434 and DMS-1601953) 2021-09-07T17:53:16Z 2019-11-08T18:37:56Z 2021-09-07T17:53:16Z 2018 2019-11-08T12:53:46Z Article http://purl.org/eprint/type/JournalArticle 0001-5962 1871-2509 https://hdl.handle.net/1721.1/122808.2 Bezrukavnikov, Roman et al. "Character bounds for finite groups of Lie type." Acta Mathematica 221, 1 (2018): 1-57. en http://dx.doi.org/10.4310/acta.2018.v221.n1.a1 Acta Mathematica Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/octet-stream International Press of Boston arXiv |
| spellingShingle | Bezrukavnikov, Roman Liebeck, Martin W. Shalev, Aner Tiep, Pham Huu Character bounds for finite groups of Lie type |
| title | Character bounds for finite groups of Lie type |
| title_full | Character bounds for finite groups of Lie type |
| title_fullStr | Character bounds for finite groups of Lie type |
| title_full_unstemmed | Character bounds for finite groups of Lie type |
| title_short | Character bounds for finite groups of Lie type |
| title_sort | character bounds for finite groups of lie type |
| url | https://hdl.handle.net/1721.1/122808.2 |
| work_keys_str_mv | AT bezrukavnikovroman characterboundsforfinitegroupsoflietype AT liebeckmartinw characterboundsforfinitegroupsoflietype AT shalevaner characterboundsforfinitegroupsoflietype AT tiepphamhuu characterboundsforfinitegroupsoflietype |