An insertion algorithm for multiplying Demazure characters by Schur polynomials

TL;DR

This paper presents a new insertion algorithm on Kohnert's model for Demazure characters, enabling explicit formulas for their products with Schur polynomials and advancing understanding of Demazure module tensor products.

Contribution

It introduces a novel insertion algorithm that generalizes RSK insertion to Demazure characters, providing explicit formulas and partially resolving Polo's conjecture.

Findings

Explicit nonnegative formula for Demazure-Schur product

Partial resolution of Polo's conjecture on Demazure modules

Generalization of RSK insertion to Kohnert's model

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.