10 a.m. - 11 a.m. Location: FO 2.208
Texas A&M University
A Murnaghan-Nakayama formula in quantum Schubert calculus
The Murnaghan-Nakayama rule expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. As the power sums generate the algebra of symmetric functions, the Murnaghan-Nakayama rule is as fundamental as the Pieri rule. Interestingly, the resulting formulas from the Murnaghan-Nakayama rule are significantly more compact than those from the Pieri formula. In geometry, a Murnaghan-Nakayama formula computes the intersection of Schubert cycles with tautological classes coming from the Chern character.
In this talk, I will discuss some background, and then some recent work establishing Murnaghan-Nakayama rules for Schubert polynomials and for quantum Schubert polynomials. This is joint work with Morrison, Benedetti, Bergeron, Colmenarejo, and Saliola.