منابع مشابه
2 Hecke Algebras with Unequal Parameters
These notes are an expanded version of the Aisenstadt lectures given at the CRM, Université de Montréal, in May/June 2002; they also include material from lectures given at MIT during the Fall of 1999 [L12]. I wish to thank Jacques Hurtubise for inviting me to give the Aisenstadt lectures. Hecke algebras arise as endomorphism algebras of representations of groups induced by representations of s...
متن کاملThe r - Polynomials in Hecke Algebras with Unequal Parameters
This paper is concerned with some important properties of r-polynomials in Hecke algebras with unequal parameters . In chapter one, we briefly introduce some conceptions in Coxeter group W and some notations in Hecke algebra H. In chapter two, we give some important properties of some r-polynomials which satisfy ry,w = ∏l(w)−l(y) i=1 (vsi − v−1 si ) when y ≤ w in W and w = s1s2 · · · sq is any ...
متن کاملRemarks on Iwahori–hecke Algebras with Unequal Parameters
By Tits’ deformation argument, a generic Iwahori–Hecke algebra H associated to a finite Coxeter group W is abstractly isomorphic to the group algebra of W . Lusztig has shown how one can construct an explicit isomorphism, provided that the Kazhdan–Lusztig basis of H satisfies certain deep properties. If W is crystallographic and H is a one-parameter algebra, then these properties are known to h...
متن کاملHecke Algebras
which is Artin’s braid relation. In general we will refer to (1) as the braid relation satisfied by si and sj. In order for W to be a Coxeter group it is required that the given set of relations between elements of I give a presentation of W . Informally, this means that any relation between generators in I can be deduced from the fact that the s ∈ Σ have order 2 and the braid relations. Formal...
متن کاملHecke group algebras as degenerate affine Hecke algebras
The Hecke group algebra H W̊ of a finite Coxeter group W̊ , as introduced by the first and last author, is obtained from W̊ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when W̊ is the classical Weyl group associated to an affine Weyl group W . Namely, we prove that, for q not a root of unity, H W̊ is the ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2015
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-015-0645-7