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

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arxiv math/0506448 v2 pith:FA3NS4TN submitted 2005-06-22 math.RT

Fokko Du Cloux (ICJ) This is my paper · ORCID
classification math.RT
keywords coxetergroupsheckepositivityalgebraalgebrasalgorithmallows
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Idempotents, traces, and dimensions in Hecke categories

    math.RT 2025-07 conditional novelty 8.0 of 10

    The paper provides closed formulas for recursible local intersection forms and recursive partial trace formulas that reduce categorical dimensions in asymptotic Hecke categories to diagrammatic computations.

  2. On Hecke and asymptotic categories for a family of complex reflection groups

    math.RT 2024-09 unverdicted novelty 6.0 of 10

    Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.

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