Laura Colmenarejo (North Carolina State University)
Title: A Murnaghan-Nakayama rule for the quantum Schubert polynomials
Abstract:聽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聳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.
Venue
UQAM, PK-5115, 201 Av. du Pr茅sident-Kennedy, Montr茅al, QC H2X 3Y7