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 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.(More)
Introduction The irreducible admissible representations of a real reductive group such as GL(n,R) have been classified by work of Langlands, Knapp, Zuckerman and Vogan. This classification is somewhat involved and requires a substantial number of prerequisites. See [13] for a reasonably accessible treatment. It is fair to say that it is difficult for a(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)
where k (p) is the +1 (−1) eigenspace of θ on g. Let Z(g) be the center of the universal enveloping algebra of g, and fix a character χ of Z(g). Let HC be the category of Harish-Chandra modules for G (i.e. finitely generated (g,K)–modules), and let HCχ be the full subcategory of HC of the modules with generalized central character χ. We are interested in(More)