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Character bounds for finite groups of Lie type

Roman Bezrukavnikov Massachusetts Institute of Technology Martin W. Liebeck Imperial College Aner Shalev Hebrew University Pham Huu Tiep Rutgers University

Arithmetic Geometry and Commutative Algebra mathscidoc:1911.43024

Acta Mathematica, 221, (1), 1 – 57, 2018
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.
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@inproceedings{roman2018character,
  title={Character bounds for finite groups of Lie type},
  author={Roman Bezrukavnikov, Martin W. Liebeck, Aner Shalev, and Pham Huu Tiep},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128112653059671535},
  booktitle={Acta Mathematica},
  volume={221},
  number={1},
  pages={1 – 57},
  year={2018},
}
Roman Bezrukavnikov, Martin W. Liebeck, Aner Shalev, and Pham Huu Tiep. Character bounds for finite groups of Lie type. 2018. Vol. 221. In Acta Mathematica. pp.1 – 57. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128112653059671535.
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