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Explicit matrices for irreducible representations of Weyl groups

Author(s): John R. Stembridge
Journal: Represent. Theory 8 (2004), 267-289.
MSC (2000): Primary 20F55, 20C40; Secondary 05E15, 20-04
Posted: July 8, 2004
Errata: Represent. Theory 10 (2006), 48
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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
Email: jrs@umich.edu

DOI: 10.1090/S1088-4165-04-00236-5
PII: S 1088-4165(04)00236-5
Received by editor(s): March 12, 2004
Posted: July 8, 2004
Additional Notes: This work was supported by NSF grants DMS--0070685 and DMS--0245385
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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