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Title: Quiver varieties and symmetric pairs
We study fixed-point loci of Nakajima varieties under symplectomorphisms and their antisymplectic cousins, which are compositions of a diagram isomorphism, a reflection functor, and a transpose defined by certain bilinear forms. These subvarieties provide a natural home for geometric representation theory of symmetric pairs. In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair. The latter symplectic subvarieties are further used to geometrically construct an action of a twisted Yangian on a torus equivariant cohomology of Nakajima varieties. In the type A case, these subvarieties provide a quiver model for partial Springer resolutions of nilpotent Slodowy slices of classical groups and associated symmetric spaces, which leads to a rectangular symmetry and a refinement of Kraft-Procesi row/column removal reductions.  more » « less
Award ID(s):
1801915
PAR ID:
10180129
Author(s) / Creator(s):
Date Published:
Journal Name:
Representation theory
Volume:
23
Issue:
2019
ISSN:
1088-4165
Page Range / eLocation ID:
1-56
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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