Combinatorics Seminar
Friday, September 14, 2018 at 4:15pm to 5:15pm
Microsoft Research, MSR First Floor Conference Center, One Memorial Dr, Cambridge, MA
SPEAKER: Frank Sottile (Texas A&M)
TITLE: A Murnaghan-Nakayama rule in quantum Schubert calculus
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 practice, it follows from the rule for multiplying schur functions for hook-shaped partitions.
In this talk, I will discuss some background, and then our work establishing a Murnaghan-Nakayama rule for quantum Schubert polynomials, which has been challenging. This is joint work with Morrison, Benedetti, Bergeron, Ccolmenarejo, and Saliola.
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