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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.


Elliptic centralizers in Weyl groups and their coinvariant representations
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by Mark Reeder
Represent. Theory 15 (2011), 63-111
Published electronically: January 24, 2011


The centralizer $C(w)$ of an elliptic element $w$ in a Weyl group has a natural symplectic representation on the group of $w$-coinvariants in the root lattice. We give the basic properties of this representation, along with applications to $p$-adic groups—classifying maximal tori and computing inducing data in $L$-packets—as well as to elucidating the structure of the centralizer $C(w)$ itself. We give the structure of each elliptic centralizer in $W(E_8)$ in terms of its coinvariant representation, and we refine Springer’s theory for elliptic regular elements to give explicit complex reflections generating $C(w)$. The case where $w$ has order three is examined in detail, with connections to mathematics of the nineteenth century. A variation of the methods recovers the subgroup $W(H_4)\subset W(E_8)$.
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Bibliographic Information
  • Mark Reeder
  • Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
  • Email:
  • Received by editor(s): June 9, 2009
  • Received by editor(s) in revised form: February 3, 2010
  • Published electronically: January 24, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Represent. Theory 15 (2011), 63-111
  • MSC (2010): Primary 11E72, 20G05, 20G25
  • DOI:
  • MathSciNet review: 2765477