Robert M. Guralnick, Michael Larsen, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig label and in terms of its degree. Then we prove explicit upper bounds for character values at elements with not-too-large centralizers and derive upper bounds on the covering number and mixing time of random walks corresponding to these conjugacy classes. We also characterize the level of the character in terms of certain dual pairs and prove explicit exponential character bounds for the character values, provided that the level is not too large. Several further applications are also provided. Related results for other finite classical groups are obtained in the sequel [Guralnick et al. 'Character levels and character bounds for finite classical groups', Preprint, 2019, arXiv:1904.08070] by different methods.

Original languageEnglish (US)
Article numbere2
JournalForum of Mathematics, Pi
StatePublished - 2020

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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