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 Kpolynomials
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 abovementioned 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 Kpolynomial of an arbitrarily oriented type A quiver locus embedded inside of its representation space. These formulas are generalizations of three of KnutsonMillerShimozono's formulas from the equioriented type A setting.
This is joint work with Ryan Kinser and Allen Knutson.
Files:
Speaker: Jenna Rajchgot
Institution: U Michigan
Event Organizer:
