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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.


Coherent IC-sheaves on type $A_{n}$ affine Grassmannians and dual canonical basis of affine type $A_{1}$
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by Michael Finkelberg and Ryo Fujita
Represent. Theory 25 (2021), 67-89
Published electronically: January 28, 2021


The convolution ring $K^{GL_n(\mathcal {O})\rtimes \mathbb {C}^\times }(\mathrm {Gr}_{GL_n})$ was identified with a quantum unipotent cell of the loop group $LSL_2$ in Cautis and Williams [J. Amer. Math. Soc. 32 (2019), pp. 709–778]. We identify the basis formed by the classes of irreducible equivariant perverse coherent sheaves with the dual canonical basis of the quantum unipotent cell.
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Bibliographic Information
  • Michael Finkelberg
  • Affiliation: Department of Mathematics, National Research University Higher School of Economics, Russian Federation, 6 Usacheva st., Moscow, Russia 119048; Skolkovo Institute of Science and Technology, Moscow, Russia; and Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
  • MR Author ID: 304673
  • Email:
  • Ryo Fujita
  • Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, Université de Paris, Bâtiment Sophie Germain, F-75013 Paris, France
  • MR Author ID: 1243866
  • Email:
  • Received by editor(s): February 27, 2019
  • Received by editor(s) in revised form: November 19, 2020
  • Published electronically: January 28, 2021
  • Additional Notes: The first author was partially funded within the framework of the HSE University Basic Research Program and the Russian Academic Excellence Project ‘5-100’. The second author was supported by Grant-in-Aid for JSPS Research Fellow (No. 18J10669) and in part by Kyoto Top Global University program.
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 67-89
  • MSC (2020): Primary 17B37, 22E67; Secondary 13F60
  • DOI:
  • MathSciNet review: 4205967