On the Distribution of the Number of Fixed Vectors for the Finite Classical Groups

Jason Fulman, Dennis Stanton

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Motivated by analogous results for the symmetric group and compact Lie groups, we study the distribution of the number of fixed vectors of a random element of a finite classical group. We determine the limiting moments of these distributions, and find exactly how large the rank of the group has to be in order for the moment to stabilize to its limiting value. The proofs require a subtle use of some q-series identities. We also point out connections with orthogonal polynomials.

Original languageEnglish (US)
Pages (from-to)755-773
Number of pages19
JournalAnnals of Combinatorics
Volume20
Issue number4
DOIs
StatePublished - Dec 1 2016

Keywords

  • finite classical group
  • fixed space

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