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Topics in Representation Theory
Refined Action of the Ring of Symmetric Functions on Fock Space
Refined Action of the Ring of Symmetric Functions on Fock Space
Organizers
Speaker
Maksim Karev
Time
Wednesday, February 12, 2025 1:00 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
There are two well-established actions of the ring of symmetric functions on Fock space. The first action is derived from the Fock space's representation as a direct sum of centers of symmetric group algebras. The second action emerges from viewing Fock space as the algebra of endomorphisms associated with the representation of the hyperoctohedral group induced to the symmetric group. In this talk, I will present a three-parameter family of representations of the ring of symmetric functions on Fock space that encompasses both of these known actions. This work is a collaboration in progress with R. Fesler, M. Hahn, and H. Markwig.