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.

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 Mathematics

References in corpus (1)

• Quiver varieties and Beilinson-Drinfeld Grassmannians of type A

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• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Singularities of nilpotent orbit closures
• Masses, Sheets and Rigid SCFTs
• Irreducible components of two-row Springer fibers and Nakajima quiver varieties
• Quiver varieties and symmetric pairs
• Group actions on quiver varieties and applications
• Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
• A study of irreducible components of Springer fibers using quiver varieties