Ottawa, June 7 - 11, 2021
I will provide a simultaneous generalization of the quotient constructions mentioned above. This generalization will be shown to have versions in the smooth, holomorphic, complex algebraic, and derived symplectic contexts. As a corollary, I will derive a concrete and Lie-theoretic construction of "universal" symplectic quotients.
This represents joint work with Maxence Mayrand.
After recalling some of this story, I will motivate and discuss the related setting of Derksen-Weyman's symmetric quivers and their representation varieties. I will show how one can adapt results from the ordinary type A setting to unify aspects of the equivariant geometry of type A symmetric quiver representation varieties with Borel orbit closures in a corresponding symmetric variety G/K (G = general linear group, K = orthogonal or symplectic group). This is joint work with Ryan Kinser and Martina Lanini.