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Positivity results for the Hecke algebras of non-crystallographic finite Coxeter groups

Fokko Du Cloux
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Abstract

This paper is a report on a computer check of some positivity properties of the Hecke algebra in type H4, including the non-negativity of the coefficients 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.

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Fokko Du Cloux. 2005-10-16. Positivity results for the Hecke algebras of non-crystallographic finite Coxeter groups. https://arxiv.org/abs/math/0506448

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