國立清華大學 數學系

Abstract: In this talk I will explain various new phenomena that arise from folding a Dynkin diagram. Since introduced by Drinfeld-Jimbo, the quantum groups have played a central role in Lie theory. By folding, one produces from the quantum groups a variant called the quantum symmetric pairs that enjoy a similar theory of canonical basis, which is an analog of the Kazhdan-Lusztig basis. On the other hand, folding of a graph induces an automorphism on Nakajima's quiver varieties which contain (type A) Springer fibers. Taking the fixed points in turn produces isomorphisms between (two-row) Springer fibers of classical types, whose structures of irreducible components are found useful in the computation of parabolic Kazhdan-Lusztig polynomials.