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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.


Integral homology of loop groups via Langlands dual groups
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by Zhiwei Yun and Xinwen Zhu
Represent. Theory 15 (2011), 347-369
Published electronically: April 20, 2011


Let $K$ be a connected compact Lie group, and $G$ its complexification. The homology of the based loop group $\Omega K$ with integer coefficients is naturally a $\mathbb {Z}$-Hopf algebra. After possibly inverting $2$ or $3$, we identify $H_*(\Omega K,\mathbb {Z})$ with the Hopf algebra of algebraic functions on $B^\vee _e$, where $B^\vee$ is a Borel subgroup of the Langlands dual group scheme $G^\vee$ of $G$ and $B^\vee _e$ is the centralizer in $B^\vee$ of a regular nilpotent element $e\in \operatorname {Lie} B^\vee$. We also give a similar interpretation for the equivariant homology of $\Omega K$ under the maximal torus action.
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Bibliographic Information
  • Zhiwei Yun
  • Affiliation: Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
  • Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • MR Author ID: 862829
  • Email:
  • Xinwen Zhu
  • Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
  • MR Author ID: 868127
  • Email:
  • Received by editor(s): September 29, 2009
  • Received by editor(s) in revised form: October 24, 2010
  • Published electronically: April 20, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 347-369
  • MSC (2010): Primary 57T10, 20G07
  • DOI:
  • MathSciNet review: 2788897