An insertion algorithm for multiplying Demazure characters by Schur polynomials

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.