On Quasi Steinberg characters of Symmetric and Alternating groups and their Double Covers

2020/09/28 by Paul, Digjoy, Singla, Pooja
#05E10 #20C25 #20C30 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2009.13412

Abstract

An irreducible character of a finite group G is called quasi p-Steinberg character for a prime p if it takes a nonzero value on every p-regular element of G. In this article, we classify the quasi p-Steinberg characters of Symmetric (S_n) and Alternating (A_n) groups and their double covers. In particular, an existence of a non-linear quasi p-Steinberg character of S_n implies n ≤ 8 and of A_n implies n ≤ 9.

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