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This paper is a report on a computer check of some important positivity properties of the Hecke algebra in type H 4 , including the non-negativity 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(More)
Let (W; S) be a Coxeter system ((1] ch. 4), where we assume S to be nite, with n elements , n 1. The theory of these groups exhibits a deep interplay between geometry and combinatorics; in fact, many basic combinatorial facts about them are most conveniently proved using an explicit geometric realization, and are best understood in that setting. This is(More)