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- Fokko du Cloux
- Eur. J. Comb.
- 2000

- Fokko du Cloux
- 2008

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)

- Fokko du Cloux
- J. Symb. Comput.
- 1999

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)

- Fokko du Cloux
- Experimental Mathematics
- 2002

- Fokko du Cloux, Jeff Adams
- 2005

These are notes for the third meeting of the Atlas of reductive Lie groups project at AIM, in Palo Alto. They describe how to take the description of the representation theory of a real reductive Lie group (cf. Jeff Adams’ notes from last year) to finite combinatorial terms, that can be implemented in a computer. These ideas evolved during my stay at MIT… (More)

- Fokko du Cloux
- Applicable Algebra in Engineering, Communication…
- 1996

We present the different approaches available today for the computation of Kazhdan-Lusztig polynomials by computer, and describe the scope of the existing programs in this area. We also outline some possible directions for future developments.

- David Alexander Vogan, Jeffrey D. Adams, +16 authors John R. Stembridge

On January 8, 2007, just before 9 in the morning, a computer finished writing to disk about sixty gigabytes of files containing the Kazhdan-Lusztig polynomials for the split real group G of type E8. Values at 1 of these polynomials are coefficients in characters of irreducible representations of G; so all irreducible characters were written down. The… (More)

- Fokko du Cloux
- 2003

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)

- J-L Riond, Nese Kocabagli, Fokko du Cloux, Mark Wanner
- The Veterinary record
- 1996