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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Quiver varieties and symmetric pairs
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by Yiqiang Li
Represent. Theory 23 (2019), 1-56
Published electronically: January 17, 2019


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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Bibliographic 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