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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.


Equivariant multiplicities of simply-laced type flag minors
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by Elie Casbi
Represent. Theory 25 (2021), 1049-1092
Published electronically: December 16, 2021


Let $\mathfrak {g}$ be a finite simply-laced type simple Lie algebra. Baumann-Kamnitzer-Knutson recently defined an algebra morphism $\overline {D}$ on the coordinate ring $\mathbb {C}[N]$ related to Brion’s equivariant multiplicities via the geometric Satake correspondence. This map is known to take distinguished values on the elements of the MV basis corresponding to smooth MV cycles, as well as on the elements of the dual canonical basis corresponding to Kleshchev-Ram’s strongly homogeneous modules over quiver Hecke algebras. In this paper we show that when $\mathfrak {g}$ is of type $A_n$ or $D_4$, the map $\overline {D}$ takes similar distinguished values on the set of all flag minors of $\mathbb {C}[N]$, raising the question of the smoothness of the corresponding MV cycles. We also exhibit certain relations between the values of $\overline {D}$ on flag minors belonging to the same standard seed, and we show that in any $ADE$ type these relations are preserved under cluster mutations from one standard seed to another. The proofs of these results partly rely on Kang-Kashiwara-Kim-Oh’s monoidal categorification of the cluster structure of $\mathbb {C}[N]$ via representations of quiver Hecke algebras.
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Bibliographic Information
  • Elie Casbi
  • Affiliation: Université de Paris, Sorbonne Université, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, F-75013 Paris, France
  • MR Author ID: 1379041
  • ORCID: 0000-0001-9064-2741
  • Email:
  • Received by editor(s): June 22, 2020
  • Received by editor(s) in revised form: August 18, 2021, August 27, 2021, and September 7, 2021
  • Published electronically: December 16, 2021
  • 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 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 1049-1092
  • MSC (2020): Primary 16G10, 20G05
  • DOI:
  • MathSciNet review: 4353894