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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.


Stable maps, Q-operators and category $\mathcal {O}$
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by David Hernandez
Represent. Theory 26 (2022), 179-210
Published electronically: March 17, 2022


Motivated by Maulik-Okounkov stable maps associated to quiver varieties, we define and construct algebraic stable maps on tensor products of representations in the category $\mathcal {O}$ of the Borel subalgebra of an arbitrary untwisted quantum affine algebra. Our representation-theoretical construction is based on the study of the action of Cartan-Drinfeld subalgebras. We prove the algebraic stable maps are invertible and depend rationally on the spectral parameter. As an application, we obtain new $R$-matrices in the category $\mathcal {O}$ and we establish that a large family of simple modules, including the prefundamental representations associated to $Q$-operators, generically commute as representations of the Cartan-Drinfeld subalgebra. We also establish categorified $QQ^*$-systems in terms of the $R$-matrices we construct.
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Bibliographic Information
  • David Hernandez
  • Affiliation: Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, IUF, F-75006 Paris, France
  • MR Author ID: 707094
  • Email:
  • Received by editor(s): April 20, 2021
  • Received by editor(s) in revised form: September 17, 2021
  • Published electronically: March 17, 2022
  • Additional Notes: The author was supported by the European Research Council under the European Union’s Framework Programme H2020 with ERC Grant Agreement number 647353 Qaffine
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 179-210
  • MSC (2020): Primary 17B37, 17B10, 82B23
  • DOI:
  • MathSciNet review: 4396040