Multiplicity-free key polynomials
Combinatorics
2023-07-10 v1
Abstract
The key polynomials, defined by A. Lascoux-M.-P. Sch\"utzenberger, are characters for the Demazure modules of type A. We classify multiplicity-free key polynomials. The proof uses two combinatorial models for key polynomials. The first is due to A. Kohnert. The second is by S. Assaf-D. Searles, in terms of quasi-key polynomials. Our argument proves a sufficient condition for a quasi-key polynomial to be multiplicity-free.
Cite
@article{arxiv.2007.09229,
title = {Multiplicity-free key polynomials},
author = {Reuven Hodges and Alexander Yong},
journal= {arXiv preprint arXiv:2007.09229},
year = {2023}
}
Comments
20 pages