Colloquium

Jenna Rajchgot, McMaster University

"Symmetric quivers and symmetric varieties"

Since the 1980s, mathematicians have found connections between orbit closures in type A quiver representation varieties and Schubert varieties in type A flag varieties. For example, singularity types appearing in type A quiver orbit closures coincide with those appearing in Schubert varieties in type A flag varieties; combinatorics of type A quiver orbit closure containment is governed by Bruhat order on the symmetric group; and formulas for classes of type A quiver orbit closures in torus equivariant cohomology and K-theory can be expressed in terms of Schubert polynomials, Grothendieck polynomials, and other objects from Schubert calculus.

In this talk, I will motivate and recall some of this story. I will then discuss the related setting of H. Derksen and J. Weyman's symmetric quivers and their representation varieties. I will show how one can adapt results from the ordinary type A quiver setting to unify aspects of the equivariant geometry of type A symmetric quiver representation varieties with Borel orbit closures in corresponding symmetric varieties G/K (G = general linear group, K = orthogonal or symplectic group). This is joint work with Ryan Kinser and Martina Lanini. 

MC 5501