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arxiv: 2411.04347 · v3 · pith:5TF5UZERnew · submitted 2024-11-07 · 🧮 math.RT · math.CO· math.PR

Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function

Lucas Teyssier , Paul Th\'evenin This is my paper
classification 🧮 math.RT math.COmath.PR
keywords boundscharactersdegreesfunctiongroupsshalevsharpsymmetric
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We prove sharp bounds on the virtual degrees introduced by Larsen and Shalev. This leads to improved bounds on characters of symmetric groups. We then sharpen bounds of Liebeck and Shalev concerning the Witten zeta function. Our main application is a characterization of the fixed-point free conjugacy classes whose associated random walk mixes in 2 steps.

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  1. Cutoff profiles for conjugacy invariant random walks on symmetric groups

    math.PR 2026-05 unverdicted novelty 7.0

    Proves Poissonian cutoff profiles for conjugacy-invariant random walks on symmetric groups with macroscopic fixed points and cutoff for random involution walks using character asymptotics.