A Virtual Character and Nonzero Kronecker Coefficients for Self-conjugate Partitions  

作　　者：Xin Li 

机构地区：[1]Department of Applied Mathematics,Zhejiang University of Technology Hangzhou 310023,China

出　　处：《Algebra Colloquium》2022年第2期321-340,共20页代数集刊（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11801506 and Grant No.11626211).

摘　　要：We generalize Regev's results on a virtual character of the symmetric group S_(n),that is,an integer-combination of some irreducible characters.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 bya concreteexample.

关 键 词：symmetric group character Kronecker coefficient NEIGHBORHOOD hooklength diagram Schur function 

分 类 号：O15[理学—数学]