# Kronecker multiplicities in the $k,ell$ hook are polynomially bounded - Mathematics > Representation Theory

Kronecker multiplicities in the $k,ell$ hook are polynomially bounded - Mathematics > Representation Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: The problem of decomposing the Kronecker product of $S n$ characters is oneof the last major open problems in the ordinary representation theory of thesymmetric group $S n$. Here we prove upper and lower polynomial bounds for themultiplicities of the Kronecker product $\chi^\lm\otimes\chi^\mu$, where forsome 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.

Author: Amitai Regev

Source: https://arxiv.org/