The stability of the Kronecker products of Schur functions
Representation Theory
2020-04-14 v2 Combinatorics
Abstract
In the late 1930's Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n for which all the coefficients of a Kronecker product of Schur functions stabilize. We also compute two new bounds for the stabilization of a sequence of coefficients and show that they improve existing bounds of M. Brion and E. Vallejo.
Cite
@article{arxiv.0907.4652,
title = {The stability of the Kronecker products of Schur functions},
author = {Emmanuel Briand and Rosa Orellana and Mercedes Rosas},
journal= {arXiv preprint arXiv:0907.4652},
year = {2020}
}
Comments
16 pages