Fokko du Cloux

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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)
This represents my attempts to digest [Kazhdan-Lusztig:1979]. My exposition will follow that paper closely, with a few ideas taken from [Soergel:1997] and [Shi:1986]. In the final section, I include an argument essentially due to Susumu Ariki to show that KL cells in S n coincide with those described by the Robinson-Schensted process. In a future version,(More)