Kronecker multiplicities in the $(k,\ell )$ hook are polynomially bounded

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 $χ^\lm\otimesχ^μ$, where for some fixed $k$ and $\ell$ both partitions $\lm$ and $\mu$ are in the $(k,\ell )$ hook, $\lm$ and $\mu$ are partitions of $n$, and $n$ goes to infinity.

Cited by in corpus (1)

• Kronecker products, characters, partitions, and the tensor square conjectures