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On the irreducible characters of Hecke algebras. (English) Zbl 0816.20034
Let \(W\) be a finite Weyl group, and \(K\) an arbitrary field. Let \(H_ K\) be the Hecke algebra associated with \(W\) over \(K\) with parameters \(q_ s\), \(s \in S\), where \(S \subset W\) is a corresponding set of simple reflections. The authors show that the values of the irreducible characters are constant on basis elements \(T_ w\), where \(w\) runs over the elements of minimal length in a given conjugacy class of \(W\), and that the values on any other basis element can be computed from these by a simple algorithm. This was first done by A. J. Starkey and A. Ram for the Hecke algebra of type \(A_ 1\).

20G05 Representation theory for linear algebraic groups
20C30 Representations of finite symmetric groups
20G40 Linear algebraic groups over finite fields
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20H15 Other geometric groups, including crystallographic groups
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