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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 of groups 20C30 Representations of finite symmetric groups