





















Abstract:Let $ \chi $ be a character of a complex irreducible representation of a finite group $G$. We present a simple formula for the expectation of the random variable $(|\chi|/\chi(1))^{t} $ in terms of character ratios $ (|\chi(g)|/\chi(1))^{t}, \; g \in G, \; t \geq 0 $. As a follow up we briefly discuss asymptotic properties of the formula and its relation to the subject of growth of dimensions of isotypic components in (virtual) tensor powers of irreducible representations. Similar type of reasoning can be applied to some questions related to commuting probability. In particular, we obtain an analogue of Frobenis formula for the probability of an "event" $ |\chi( [x,y]^{-1}g)| = r $
From: Alexander Kushkuley [view email]
[v1]
Tue, 24 Mar 2026 18:02:25 UTC (65 KB)
[v2]
Tue, 26 May 2026 20:14:54 UTC (31 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。