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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089-2532, USA

    Jason Fulman

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Dennis Stanton

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  1. Jason Fulman
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  2. Dennis Stanton
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Correspondence to Dennis Stanton.

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Fulman, J., Stanton, D. On the Distribution of the Number of Fixed Vectors for the Finite Classical Groups. Ann. Comb. 20, 755–773 (2016). https://doi.org/10.1007/s00026-016-0336-7

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  • DOI: https://doi.org/10.1007/s00026-016-0336-7

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