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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Explicit matrices for irreducible representations of Weyl groups
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by John R. Stembridge PDF
Represent. Theory 8 (2004), 267-289 Request permission

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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Additional 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