| Abstract: 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. Interesting, 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. |