Algebraic and Enumerative Combinatorics Seminar - Kelvin Chan

Thursday, November 30, 2023 2:00 pm - 2:00 pm EST (GMT -05:00)

Title: Polarization operators in superspace

Speaker: Kelvin Chan
Affiliation: York University
Location: MC 6029

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:00 pm.

Abstract: The classic coinvariant space is a graded representation of the symmetric group with deep connections to permutation statistics and Hall-Littlewood polynomials. Its generalization, the diagonal harmonics, has a rich connection to Macdonald polynomials and the q,t-Catalan numbers. In this talk, we consider the variant of the classical coinvariant story in the superspace. We briefly survey its connections and recent developments. We introduce polarization operators and discuss a new basis for its alternating component. We also discuss a folklore on cocharge and propose a basis for the super harmonics.