Diagram automorphisms of quiver varieties

作者：Henderson Anthony^*; Licata Anthony

来源：Advances in Mathematics, 2014, 267: 225-276.

DOI：10.1016/j.aim.2014.08.007

• Quiver varieties
• Automorphisms
• Springer resolution
• Slodowy slices

We show that the fixed-point subvariety of a Nakajima quiver variety under a diagram automorphism is a disconnected union of quiver varieties for the 'split-quotient quiver' introduced by Reiten and Riedtmann. As a special case, quiver varieties of type D arise as the connected components of fixed-point subvarieties of diagram involutions of quiver varieties of type A. In the case where the quiver varieties of type A correspond to small self-dual representations, we show that the diagram involutions coincide with classical involutions of tworow Slodowy varieties. It follows that certain quiver varieties of type D are isomorphic to Slodowy varieties for orthogonal or symplectic Lie algebras.

• 出版日期2014-12-20