Character bounds for finite groups of Lie type
Name
1707.03896.pdf
Description
Accepted version
Size
558.7 KB
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Unknown
Checksum (MD5)
a22050c58aa1b5c6d9b98ad2b768b5ae
Author(s)
Bezrukavnikov, Roman
Liebeck, Martin W.
Shalev, Aner
Tiep, Pham Huu
Date Issued
2018
Journal
Acta Mathematica
Publisher
International Press of Boston
Citation
Bezrukavnikov, Roman et al. "Character bounds for finite groups of Lie type." Acta Mathematica 221, 1 (2018): 1-57.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4310/acta.2018.v221.n1.a1
