The stability of the Kronecker products of Schur functions

Details The stability of the Kronecker products of Schur functions The stability of the Kronecker products of Schur functions

2009-07-27

arxiv.org/abs/0907.4652v2

Mathematics

Representation Theory

16 pages

Scientific paper

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.

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