The down operator and expansions of near rectangular k-Schur functions
Combinatorics
2012-02-20 v3
Abstract
We prove that the Lam-Shimozono "down operator" on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of "near rectangles" in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of the corresponding k-Littlewood--Richardson coefficients.
Keywords
Cite
@article{arxiv.1112.4460,
title = {The down operator and expansions of near rectangular k-Schur functions},
author = {Chris Berg and Franco Saliola and Luis Serrano},
journal= {arXiv preprint arXiv:1112.4460},
year = {2012}
}