Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Hugh THOMAS - New Brunswick et Bonn,
Titre ``Dual'' Garside structures for finite-type Artin groups via quiver representations
Horaire14:30 à 15:30
RésumeThe Artin groups of type A are the braid groups; for any Coxeter group, there is an associated Artin group, which is called finite type if the Coxeter group is finite.There is a standard presentation for Artin group analogous to the standard presentation for Coxeter groups. A useful property of the standard presentation for Artin groups of finite type is that there is an associated Garside structure. This gives, for example, an algorithm for computing a normal form for elements of the Artin group. \par Bessis introduced a ``dual'' presentation for finite type Artin groups (extending work of Birman-Ko-Lee in type A) which also has this Garside property, and which is, in some respects, computationally preferable. The proofs of Bessis's results make use of type-by-type arguments and computer checks for the exceptional types. I will explain an alternative approach to this Garside structure (in crystallographic cases only) using the representation theory of Dynkin quivers in which the proofs are carried out in a uniform way. Time permitting, I will also discuss conjectural applications to non-finite-type Artin groups.