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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.


Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types
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by Ryo Fujita
Represent. Theory 26 (2022), 211-263
Published electronically: March 18, 2022


For a Dynkin quiver $Q$ (of type $\mathrm {ADE}$), we consider a central completion of the convolution algebra of the equivariant $K$-group of a certain Steinberg type graded quiver variety. We observe that it is affine quasi-hereditary and prove that its category of finite-dimensional modules is identified with a block of Hernandez-Leclerc’s monoidal category $\mathcal {C}_{Q}$ of modules over the quantum loop algebra $U_{q}(L\mathfrak {g})$ via Nakajima’s homomorphism. As an application, we show that Kang-Kashiwara-Kim’s generalized quantum affine Schur-Weyl duality functor gives an equivalence between the category of finite-dimensional modules over the quiver Hecke algebra associated with $Q$ and Hernandez-Leclerc’s category $\mathcal {C}_{Q}$, assuming the simpleness of some poles of normalized $R$-matrices for type $\mathrm {E}$.
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Bibliographic Information
  • Ryo Fujita
  • Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Oiwake-Kitashir- akawa, Sakyo, Kyoto 606-8502, Japan; and Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université de Paris, F-75013 Paris, France
  • MR Author ID: 1243866
  • ORCID: 0000-0003-4905-2402
  • Email:
  • Received by editor(s): November 11, 2017
  • Received by editor(s) in revised form: August 9, 2019
  • Published electronically: March 18, 2022
  • Additional Notes: The work of the author was supported in part by the Kyoto Top Global University program. It was also supported by Grant-in-Aid for JSPS Research Fellow (No. 18J10669) and by JSPS Overseas Research Fellowships during the revision.
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 211-263
  • MSC (2020): Primary 17B37; Secondary 17B67
  • DOI:
  • MathSciNet review: 4396615