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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.


The Jordan–Chevalley decomposition for $G$-bundles on elliptic curves
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by Dragoş Frăţilă, Sam Gunningham and Penghui Li
Represent. Theory 26 (2022), 1268-1323
Published electronically: December 21, 2022


We study the moduli stack of degree $0$ semistable $G$-bundles on an irreducible curve $E$ of arithmetic genus $1$, where $G$ is a connected reductive group in arbitrary characteristic. Our main result describes a partition of this stack indexed by a certain family of connected reductive subgroups $H$ of $G$ (the $E$-pseudo-Levi subgroups), where each stratum is computed in terms of $H$-bundles together with the action of the relative Weyl group. We show that this result is equivalent to a Jordan–Chevalley theorem for such bundles equipped with a framing at a fixed basepoint. In the case where $E$ has a single cusp (respectively, node), this gives a new proof of the Jordan–Chevalley theorem for the Lie algebra $\mathfrak {g}$ (respectively, algebraic group $G$).

We also provide a Tannakian description of these moduli stacks and use it to show that if $E$ is not a supersingular elliptic curve, the moduli of framed unipotent bundles on $E$ are equivariantly isomorphic to the unipotent cone in $G$. Finally, we classify the $E$-pseudo-Levi subgroups using the Borel–de Siebenthal algorithm, and compute some explicit examples.

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Bibliographic Information
  • Dragoş Frăţilă
  • Affiliation: IRMA 7 rue René Descartes, Strasbourg, France
  • MR Author ID: 847965
  • Email:
  • Sam Gunningham
  • Affiliation: Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717
  • MR Author ID: 1178001
  • Email:
  • Penghui Li
  • Affiliation: YMSC, Tsinghua University, Beijing, People’s Republic of China
  • MR Author ID: 1340873
  • Email:
  • Received by editor(s): October 16, 2020
  • Received by editor(s) in revised form: July 28, 2022, August 17, 2022, and August 19, 2022
  • Published electronically: December 21, 2022
  • Additional Notes: The second author was partially supported by Royal Society grant RGF\textbackslash EA\textbackslash181078, the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 637618), and NSG grant DMS-2202363. The third author was partially supported by the National Natural Science Foundation of China (Grant No. 12101348).
  • © Copyright 2022 Copyright by the authors
  • Journal: Represent. Theory 26 (2022), 1268-1323
  • MSC (2020): Primary 14D20, 14D23, 14D24, 22E57
  • DOI:
  • MathSciNet review: 4524601