Affiliation:
1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
Abstract
We generalize Regev's results on a virtual character of the symmetric group [Formula: see text], that is, an integer-combination of some irreducible characters. Suppose that [Formula: see text] and [Formula: see text] are integer partitions of [Formula: see text]. For the associated irreducible character [Formula: see text] of [Formula: see text], when [Formula: see text], we find another partition [Formula: see text] related to [Formula: see text] such that [Formula: see text] 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.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory