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...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.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11801506 and Grant No.11626211).
文摘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.
