|Date: Friday, January 22, 2016
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Three combinatorial formulas for type A quiver polynomials and K-polynomials
Abstract: I'll describe a closed immersion from each representation space of a type A quiver with bipartite (i.e., alternating) orientation to a certain opposite Schubert cell of a partial flag variety. This "bipartite Zelevinsky map" restricts to an isomorphism from each orbit closure to a Schubert variety intersected with the above-mentioned opposite Schubert cell. For type A quivers of arbitrary orientation, I'll discuss a similar result up to some factors of general linear groups.
Using these identifications, I'll explain how one can obtain various combinatorial formulas for the quiver polynomial and K-polynomial of an arbitrarily oriented type A quiver locus embedded inside of its representation space. These formulas are generalizations of three of Knutson-Miller-Shimozono's formulas from the equioriented type A setting.
This is joint work with Ryan Kinser and Allen Knutson.
Speaker: Jenna Rajchgot
Institution: U Michigan