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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Quiver varieties and symmetric pairs
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by Yiqiang Li PDF
Represent. Theory 23 (2019), 1-56 Request permission


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.
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Additional Information
  • Yiqiang Li
  • Affiliation: Department of Mathematics, University at Buffalo, the State University of New York, Buffalo, New York 14260
  • MR Author ID: 828279
  • ORCID: 0000-0003-4608-3465
  • Email:
  • Received by editor(s): January 15, 2018
  • Received by editor(s) in revised form: October 15, 2018, and November 2, 2018
  • Published electronically: January 17, 2019
  • Additional Notes: This work was partially supported by the National Science Foundation under the grant DMS 1801915.
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 1-56
  • MSC (2010): Primary 16S30, 14J50, 14L35, 51N30, 53D05
  • DOI:
  • MathSciNet review: 3900699