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Diagram automorphisms of quiver varieties

Abstract

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 two-row Slodowy varieties. It follows that certain quiver varieties of type D are isomorphic to Slodowy varieties for orthogonal or symplectic Lie algebras.Comment: 43 pages. In version 2, at the referee's suggestion, we slightly expand some statements (Theorem 1.2 and Proposition 3.19) to include the relevant affine varieties. This version is to appear in Advances in Mathematic

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