Positivity results for the Hecke algebras of non-crystallographic finite Coxeter groups
نویسنده
چکیده
This paper is a report on a computer check of some important positivity properties of the Hecke algebra in type H4, including the nonnegativity of the structure constants in the Kazhdan-Lusztig basis. This answers a long-standing question of Lusztig’s. The same algorithm, carried out by hand, also allows us to deal with the case of dihedral Coxeter groups. 1 Statement of the problem 1.1. Let W be a Coxeter group, S its set of distinguished generators, and denote ≤ the Bruhat ordering on W . Denote H the Hecke algebra of W over the ring of Laurent polynomials A = Z[v, v−1], where v is an indeterminate. We refer to [3] for basic results about Coxeter groups and Hecke algebras; we just recall here that H is a free A-module with basis (ty)y∈W , where the algebra structure is the unique one which satisfies
منابع مشابه
in Algebra . Coxeter groups and Hecke algebras
The finite Coxeter groups are the finite groups generated by reflections on real Euclidean spaces. Examples include dihedral groups, the symmetry groups of regular polytopes (e.g. regular polygons and platonic solids) and the Weyl groups of semisimple complex Lie groups and Lie algebras (such as the special linear group and Lie algebra). General Coxeter groups may be defined as certain (special...
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