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A Hecke Algebra Quotient and Some Combinatorial Applications
Authors:C.K. Fan
Affiliation:(1) Math Department, Harvard University, 02138 Cambridge, MA
Abstract:Let (W, S) be a Coxeter group associated to a Coxeter graph which has no multiple bonds. Let H be the corresponding Hecke Algebra. We define a certain quotient -H of H and show that it has a basis parametrized by a certain subset Wcof the Coxeter group W. Specifically, Wcconsists of those elements of W all of whose reduced expressions avoid substrings of the form sts where s and t are noncommuting generators in S. We determine which Coxeter groups have finite Wcand compute the cardinality of Wcwhen W is a Weyl group. Finally, we give a combinatorial application (which is related to the number of reduced expressions for w isin Wcof an exponential formula of Lusztig which utilizes a specialization of a subalgebra of -H.
Keywords:permutation  representation theory  non-commutative algebra  Lie theory  reductive group
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