Kronecker multiplicities in the (k,ℓ) hook are polynomially bounded

2010/11/07 by Regev, Amitai · 1 citation
#05A17 #20C30 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1011.1636

Abstract

The problem of decomposing the Kronecker product of S_n characters is one of the last major open problems in the ordinary representation theory of the symmetric group S_n. Here we prove upper and lower polynomial bounds for the multiplicities of the Kronecker product χ^\lm⊗χ^μ, where for some fixed k and ℓ both partitions \lm and μ are in the (k,ℓ) hook, \lm and μ are partitions of n, and n goes to infinity.

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• Introduction to finite Coxeter groups and their representations

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