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Dimension-independent statistics of $ \operatorname{Gl}_n(\operatorname{\mathbb{F}_q})$ via character polynomials


Author: Nir Gadish
Journal: Proc. Amer. Math. Soc. 148 (2020), 1043-1047
MSC (2010): Primary 05E15, 20B25; Secondary 20J99
DOI: https://doi.org/10.1090/proc/14781
Published electronically: November 4, 2019
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Abstract: Picking permutations at random, the expected number of $ k$-cycles is known to be $ 1/k$ and is, in particular, independent of the size of the permuted set. This short note gives similar size-independent statistics of finite general linear groups: ones that depend only on small minors. The proof technique uses combinatorics of categories, motivated by representation stability, and applies simultaneously to symmetric groups, finite linear groups, and many other settings.


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Additional Information

Nir Gadish
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: nirg@math.uchicago.edu

DOI: https://doi.org/10.1090/proc/14781
Received by editor(s): May 19, 2019
Received by editor(s) in revised form: July 22, 2019
Published electronically: November 4, 2019
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2019 American Mathematical Society