Regular theory in complex braid groups

GARNIER, Owen

doi:10.1016/j.jalgebra.2022.12.031

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Coxeter Groups and Artin Groups1

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2023

2024

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“…Following the work of Bessis in [Bes15, Section 11], this description gives rise to a Garside category C 31 , whose envelopping groupoid B 31 is equivalent to B 31 . A detailed description of this category can be found in [Gar23].…”

Section: Coxeter Groups and Artin Groupsmentioning

confidence: 99%

Generalization of the Dehornoy-Lafont order complex to categories. Application to exceptional braid groups

Owen¹

2023

Preprint

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The homology of a Garside monoid, thus of a Garside group, can be computed efficiently through the use of the order complex defined by Dehornoy and Lafont. We construct a categorical generalization of this complex and we give some computational techniques which are useful for reducing computing time.We then use this construction to complete results of Salvetti, Callegaro and Marin regarding the homology of exceptional complex braid groups. We most notably study the case of the Borchardt braid group B(G31) through its associated Garside category. Contents 15 3.4. Well-generated exceptional groups 16 3.5. The Borchardt braid group B 31 17 3.6. Computational results 17 References 22

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Section: Coxeter Groups and Artin Groupsmentioning

confidence: 99%

Generalization of the Dehornoy-Lafont order complex to categories. Application to exceptional braid groups

Owen¹

2023

Preprint

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Combinatorics and braid varieties

Williams

2024

Proceedings of Symposia in Pure Mathematics

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I summarize a framework for finding and proving interesting combinatorial formulas using braid varieties. The combinatorics comes from the Deodhar decomposition of these braid varieties, while the enumeration uses traces in Hecke algebras to compute the number of points in these varieties over finite fields. I give several examples of the success of this framework, and also give many open problems.

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Regular theory in complex braid groups

Cited by 2 publications

References 17 publications

Generalization of the Dehornoy-Lafont order complex to categories. Application to exceptional braid groups

Generalization of the Dehornoy-Lafont order complex to categories. Application to exceptional braid groups

Combinatorics and braid varieties

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