Towards spetses. I. (English) Zbl 0972.20024

Rational reflection groups occur naturally as Weyl groups of reductive algebraic groups over finite fields. The authors conjecture that complex reflection groups are similarly related to some as yet undiscovered objects which they call spetses.
To prepare the search for spetses, the authors collect technical results on many subjects like braid groups, generic Hecke algebras, reflection data, cyclotomic specializations of Hecke algebras, spetsial cyclotomic Hecke algebras. They obtain families of unipotent characters for spetses.


20F55 Reflection and Coxeter groups (group-theoretic aspects)
20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
20C08 Hecke algebras and their representations
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