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Representations of Weyl groups of type \(B\) induced from centralisers of involutions. (English) Zbl 0738.20007

Summary: 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 \(\pi_ t\) of the centraliser of \(t\) in \(G\), such that the sum of the characters of \(G\) induced from the \(\pi_ t\) 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.

MSC:

20C15 Ordinary representations and characters
20C30 Representations of finite symmetric groups
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References:

[1] Isaacs, Character theory of finite groups (1976) · Zbl 0337.20005
[2] DOI: 10.1016/0021-8693(75)90131-3 · Zbl 0296.20004 · doi:10.1016/0021-8693(75)90131-3
[3] DOI: 10.1007/BF01188521 · Zbl 0695.20008 · doi:10.1007/BF01188521
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