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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.


Explicit matrices for irreducible representations of Weyl groups
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by John R. Stembridge
Represent. Theory 8 (2004), 267-289
Published electronically: July 8, 2004

Erratum: Represent. Theory 10 (2006), 48-48.


We present algorithms for constructing explicit matrices for every irreducible representation of a Weyl group, with particular emphasis on the exceptional groups. The algorithms we present will produce representing matrices in either of two forms: real orthogonal, with matrix entries that are square roots of rationals, or rational and seminormal. In both cases, the matrices are “hereditary” in the sense that they behave well with respect to restriction along a chosen chain of parabolic subgroups.
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Bibliographic Information
  • John R. Stembridge
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1109
  • Email:
  • Received by editor(s): March 12, 2004
  • Published electronically: July 8, 2004
  • Additional Notes: This work was supported by NSF grants DMS–0070685 and DMS–0245385
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 8 (2004), 267-289
  • MSC (2000): Primary 20F55, 20C40; Secondary 05E15, 20-04
  • DOI:
  • MathSciNet review: 2077483