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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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Quasi-split symmetric pairs of $\mathrm {U}(\mathfrak {sl}_n)$ and Steinberg varieties of classical type
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by Yiqiang Li PDF
Represent. Theory 25 (2021), 903-934 Request permission

Abstract:

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type $A_{n-1}$. This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of $n$-step isotropic flag varieties. Arising from the construction are a basis of homological origin for the idempotent form and a geometric realization of rational modules.
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Additional Information
  • Yiqiang Li
  • Affiliation: Department of Mathematics, University at Buffalo, The State University of New York, 244 Mathematics Building, Buffalo, New York 14260
  • MR Author ID: 828279
  • ORCID: 0000-0003-4608-3465
  • Email: yiqiang@buffalo.edu
  • Received by editor(s): January 17, 2020
  • Received by editor(s) in revised form: February 7, 2021
  • Published electronically: October 21, 2021
  • Additional Notes: This work was partially supported by the NSF grant DMS-1801915.
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 903-934
  • MSC (2020): Primary 17B35, 51N30
  • DOI: https://doi.org/10.1090/ert/570
  • MathSciNet review: 4329193