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Representation Theory

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Explicit matrices for irreducible representations of Weyl groups

Author: John R. Stembridge
Journal: Represent. Theory 8 (2004), 267-289
MSC (2000): Primary 20F55, 20C40; Secondary 05E15, 20-04
Published electronically: July 8, 2004
Erratum: Represent. Theory 10 (2006), 48-48.
MathSciNet review: 2077483
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Abstract: 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

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
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.