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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.


Geometrizing the minimal representations of even orthogonal groups
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by Vincent Lafforgue and Sergey Lysenko
Represent. Theory 17 (2013), 263-325
Published electronically: May 28, 2013


Let $X$ be a smooth projective curve. Write $\mathrm {Bun}_{\mathrm {S}\mathbb {O}_{2n}}$ for the moduli stack of $\mathrm {S}\mathbb {O}_{2n}$-torsors on $X$. We give a geometric interpretation of the automorphic function $f$ on $\mathrm {Bun}_{\mathrm {S}\mathbb {O}_{2n}}$ corresponding to the minimal representation. Namely, we construct a perverse sheaf $\mathcal {K}_H$ on $\mathrm {Bun}_{\mathrm {S}\mathbb {O}_{2n}}$ such that $f$ should be equal to the trace of the Frobenius of $\mathcal {K}_H$ plus some constant function. The construction is based on some explicit geometric formulas for the Fourier coefficients of $f$ on one hand, and on the geometric theta-lifting on the other hand. Our construction makes sense for more general simple algebraic groups, we formulate the corresponding conjectures. They could provide a geometric interpretation of some unipotent automorphic representations in the framework of the geometric Langlands program.
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Bibliographic Information
  • Vincent Lafforgue
  • Affiliation: CNRS et MAPMO, UMR 7349, Université d’Orléans, Rue de Chartres, B.P. 6759 - 45067 Orléans cedex 2, France
  • Email:
  • Sergey Lysenko
  • Affiliation: Institut Elie Cartan Nancy, Université de Lorraine, B.P. 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France
  • MR Author ID: 614865
  • Email:
  • Received by editor(s): April 22, 2011
  • Received by editor(s) in revised form: February 7, 2012, and November 26, 2012
  • Published electronically: May 28, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 17 (2013), 263-325
  • MSC (2010): Primary 14D24; Secondary 22E57, 11R39
  • DOI:
  • MathSciNet review: 3057297