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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
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:
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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