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

DOI:
https://doi.org/10.1090/S1088-4165-04-00236-5

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

Email:
jrs@umich.edu

DOI:
https://doi.org/10.1090/S1088-4165-04-00236-5

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.