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A Hecke algebra quotient and some combinatorial applications. (English) Zbl 0853.20028
Let $$W$$ be a Coxeter group associated to a Coxeter graph which has no multiple bonds, and $$H$$ be the corresponding Hecke algebra. The author defines a certain quotient $$\widetilde H$$ of $$H$$ and shows that it has a basis parametrized by a certain subset $$W_c$$ of the Coxeter group $$W$$, then determines which Coxeter groups have finite $$W_c$$ and computes the cardinality of $$W_c$$ when $$W$$ is a Weyl group. Finally, he gives a combinatorial application of an exponential formula of Lusztig which utilizes a specialization of a subalgebra of $$\widetilde H$$.

##### MSC:
 20F55 Reflection and Coxeter groups (group-theoretic aspects) 05A19 Combinatorial identities, bijective combinatorics
##### Keywords:
Coxeter graphs; Hecke algebras; Coxeter groups; Weyl groups
Full Text:
##### References:
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