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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 π t of the centraliser of t in G, such that the sum of the characters of G induced from the π 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:
20C15Ordinary representations and characters of groups
20C30Representations of finite symmetric groups