An insertion algorithm for multiplying Demazure characters by Schur polynomials

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.

23 pages, 16 (colored) figures plus an appendix with additional examples

References in corpus (3)

• Demazure crystals for Kohnert polynomials
• A bijective proof of Kohnert's rule for Schubert polynomials
• A Pieri rule for Demazure characters of the general linear group