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Representations of Weyl groups of type B induced from centralisers of involutions
Published online by Cambridge University Press: 17 April 2009
Abstract
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Let G be a Weyl group of type B, and T a set of representatives of the conjugacy classes of self-inverse elements of G. For each t in T, we construct a (complex) linear character πt of the centraliser of t in G, such that the sum of the characters of G induced from the πt contains each irreducible complex character of G with multiplicity precisely 1. For Weyl groups of type A (that is, for the symmetric groups), a similar result was published recently by Inglis, Richardson and Saxl.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 337 - 344
- Copyright
- Copyright © Australian Mathematical Society 1991
References
[1]Baddeley, R.W., ‘Models and involution models for wreath products and certain Weyl groups’ (Cambridge), (preprint).Google Scholar
[2]Inglis, N.F.J., Richardson, R.W. and Saxl, J., ‘An explicit model for the complex representations of Sn’, Arch. Math. 54 (1990), 258–259.CrossRefGoogle Scholar
[4]Mayer, S.J., ‘On the characters of the Weyl group of type C’, J. Algebra 33 (1975), 59–67.CrossRefGoogle Scholar
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