A virtual character and nonzero Kronecker coefficients for self-conjugate partitions

Abstract

We generalize Regev's result on a virtual character of S n . Suppose that λ and µ are integer partitions of n. For the associated irreducible character χ λ of S n , when χ λ (µ) 0 we find another partition τ related to λ such that χ τ (µ) 0 by the virtual character. Applying this result, we obtain a class of nonzero Kronecker coefficients by Pak et al.'s character criterion. Moreover, we discuss the effectiveness of Pak et al.'s character criterion by a concrete example.