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Minimal length elements in twisted conjugacy classes of finite Coxeter groups. (English) Zbl 1042.20026
Summary: Let \(W\) be a finite Coxeter group and let \(F\) be an automorphism of \(W\) that leaves the set of generators of \(W\) invariant. We establish certain properties of elements of minimal length in the \(F\)-conjugacy classes of \(W\) that allow us to define character tables for the corresponding twisted Iwahori-Hecke algebras. These results are extensions of results obtained by Geck and Pfeiffer in the case where \(F\) is trivial.

MSC:
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20E45 Conjugacy classes for groups
20C08 Hecke algebras and their representations
Software:
CHEVIE; GAP; Maple
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References:
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