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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
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.