Events

Laura Colmenarejo

NC State University
Colloquia
https://sites.google.com/view/l-colmenarejo/home

When

Date: Wednesday, September 6, 2023
Time: 3:30 pm - 5:00 pm
Location: Petty 150

Several linear algebra problems are very interesting in the ring of symmetric polynomials. One of them is understanding combinatorially how to multiply polynomials from different bases and expand the resulting symmetric polynomial in one of the bases. The classical Murnaghan–Nakayama rule is a formula for the product of a Schur symmetric polynomial and a Newton power sum. It is as fundamental as the Pieri rule, and the resulting formulas from the Murnaghan-Nakayama rule are significantly more compact. The Schubert polynomials are a very interesting generalization of Schur polynomials due to their connection with the cohomology of the flag variety in algebraic geometry. In this talk, I will present a general rule for multiplying a quantum Schubert polynomial by a quantum power sum polynomial, achieved by relating the structure constants to the classical case. We will review the classical and quantum stories and discover the combinatorics behind each version.​
This project is joint work with Carolina Benedetti, Nantel Bergeron, Franco Saliola, and Frank Sottile.