Sami Assaf (part2) "An insertion algorithm for multiplying Schubert by Schur polynomials"
Channel: Schubert Seminar
Date: 2023-03-27

Abstract: I recently conjectured a combinatorial rule for the Schubert expansion of the product of a Schubert polynomial with a Schur polynomial by counting certain saturated chains in k-Bruhat order. In this talk, I’ll present joint with work Nantel Bergeron in which we prove the formula. Inspired by my recent insertion algorithm for Demazure characters, our purely combinatorial proof comes via an explicit insertion algorithm on Kohnert diagrams, combinatorial objects which generate Schubert polynomials. Generalizing the classical Littlewood—Richardson rule, when specializing to the case of the product of two Schur polynomials with the same number of variables, our proof reduces to the Robinson--Schensted--Knuth insertion algorithm on semi-standard Young tableaux.