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- Fokko du Cloux
- 2008

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)

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

- 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, 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
- Experimental Mathematics
- 2002

- Jeffrey Adams, David Vogan, +19 authors Gregg Zuckerman
- 2009

- Fokko du Cloux
- Appl. Algebra Eng. Commun. Comput.
- 1996

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)