A Hecke Algebra quotient and some combinatorial applications
نویسندگان
چکیده
منابع مشابه
A Hecke Algebra Quotient and Some Combinatorial Applications
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 Wc of the Coxeter group w. Specifically, Wc consists of those elements of W all of whose reduced expressions avoid substrings of the form sts where s and t are noncommu...
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Let W be a Coxeter group with Coxeter graph Γ. Let H be theassociated Hecke algebra. We define a certain ideal I in H and study thequotient algebra H̄ = H/I. We show that when Γ is one of the infinite seriesof graphs of type E, the quotient is semi-simple. We examine the cell structuresof these algebras and construct their irreducible representations. We discussthe case where...
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Let i = 1 + q + · · · + qi−1. For certain sequences (r1, . . . , rl) of positive integers, we show that in the Hecke algebra Hn(q) of the symmetric group Sn, the product (1 + r1Tr1) · · · (1 + rlTrl) has a simple explicit expansion in terms of the standard basis {Tw}. An interpretation is given in terms of random walks on Sn.
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1 The affine Hecke algebra 1.1 The alcove walk algebra Fix notations for the Weyl group W , the extended affine Weyl group W , and their action on Ω × h * R as in Section 2. Label the walls of the alcoves so that the fundamental alcove has walls labeled 0, 1,. .. , n and the labeling is W-equivariant (see the picture in (2.12)). The periodic orientation is the orientation of the walls of the al...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 1996
ISSN: 0925-9899,1572-9192
DOI: 10.1007/bf00243786