Type D quiver representation varieties, double Grassmannians, and symmetric varieties Speaker(s): Jenna Rajchgot
Abstract: 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 (BobinskiZwara); combinatorics of type A quiver orbit closure containment is governed by Bruhat order on the symmetric group (follows from work of Zelevinsky, KinserR); and multiple researchers have produced formulas for classes of type A quiver orbit closures in equivariant cohomology and Ktheory in terms of Schubert polynomials, Grothendieck polynomials, and related objects.
After recalling some of this type A story, I will discuss joint work with Ryan Kinser on type D quiver representation varieties. I will describe explicit embeddings which completes a circle of links between orbit closures in type D quiver representation varieties, Borbit closures (for a Borel subgroup B of GL_n) in certain symmetric varieties GL_n/K, and Borbit closures in double Grassmannians Gr(a, n) x Gr(b, n). I will end with some geometric and combinatorial consequences, as well as a brief discussion of joint work in progress with Zachary Hamaker and Ryan Kinser on formulas for classes of type D quiver orbit closures in equivariant cohomology.
Date: 23/06/2020  2:00 pm
Collection: Geometric Representation Theory
