Absolute values and tensor powers of irreducible characters

arXiv:2603.23614v1 Announce Type: new
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 growth of dimensions of isotypic components in (virtual) tensor powers of irreducible representations