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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.


Mirković-Vilonen cycles and polytopes for a symmetric pair
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by Jiuzu Hong
Represent. Theory 13 (2009), 19-32
Published electronically: February 13, 2009


Let $G$ be a connected, simply-connected, and almost simple algebraic group, and let $\sigma$ be a Dynkin automorphism on $G$. Then $(G,G^\sigma )$ is a symmetric pair. In this paper, we get a bijection between the set of $\sigma$-invariant MV cycles (polytopes) for $G$ and the set of MV cycles (polytopes) for $G^\sigma$, which is the fixed point subgroup of $G$; moreover, this bijection can be restricted to the set of MV cycles (polytopes) in irreducible representations. As an application, we obtain a new proof of the twining character formula.
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Bibliographic Information
  • Jiuzu Hong
  • Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
  • Address at time of publication: School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
  • MR Author ID: 862719
  • Email:
  • Received by editor(s): May 13, 2008
  • Received by editor(s) in revised form: November 15, 2008
  • Published electronically: February 13, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 13 (2009), 19-32
  • MSC (2000): Primary 20G05; Secondary 14M15
  • DOI:
  • MathSciNet review: 2480386