Yiqiang Li – Geometric Methods in Representation Theory

Title: Quiver varieties and symmetric pairs

Abstract: To a simply-laced Dynkin diagram, one can attach a complex simple Lie algebra, say g, and a class of Nakajima (quiver) varieties. The latter provides a natural home for a geometric representation theory of the former. If the algebra g is further equipped with an involution, it leads to a so-called symmetric pair (g,k), where k is the fixed-point subalgebra under involution. In this talk, I’ll present a recent study of fixed-point loci of Nakajima varieties under certain involutions and provide bridges at several levels between symmetric pairs and Nakajima varieties.