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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 $$A_ 1$$.

##### MSC:
 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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