Normality of orbit closures in the enhanced nilpotent cone

Abstract

We continue the study of the closures of $GL(V)$-orbits in the enhanced nilpotent cone $V\times\cN$ begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably-defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.

30 pages

References in corpus (5)

• Orbit closures in the enhanced nilpotent cone
• An exotic Deligne-Langlands correspondence for symplectic groups
• Mirabolic affine Grassmannian and character sheaves
• Deformations of nilpotent cones and Springer correspondences
• Enhanced Nilpotent Representations of a Cyclic Quiver

Cited by in corpus (3)

• The exotic Robinson-Schensted correspondence
• On enhanced reductive groups (II): Finiteness of nilpotent orbits under enhanced group action and their closures
• Enhanced adjoint action and their orbits for the general linear group