An insertion algorithm for multiplying Demazure characters by Schur polynomials
Combinatorics
2023-04-04 v2 Algebraic Geometry
Representation Theory
Abstract
We introduce an insertion algorithm on Kohnert's combinatorial model for Demazure characters, generalizing Robinson--Schensted--Knuth insertion on tableaux. Our new insertion yields an explicit, nonnegative formula expressing the product of a Demazure character and a Schur polynomial as a sum of Schubert characters, partially resolving Polo's conjecture that the tensor product of Demazure modules admits a Schubert filtration.
Cite
@article{arxiv.2109.05651,
title = {An insertion algorithm for multiplying Demazure characters by Schur polynomials},
author = {Sami H. Assaf},
journal= {arXiv preprint arXiv:2109.05651},
year = {2023}
}
Comments
23 pages, 16 (colored) figures plus an appendix with additional examples