Monday, March 9, 2015 at 2:30 PM in SAS 4201
Christophe Hohlweg, LaCIM at Universit du Qubec Montral
Artin-Tits Braid groups, low elements and weak order in Coxeter groups
In this talk we will explain that the question of solving the conjugacy problem in the context of a general Artin-Tits Braid group reveals
strong connections between the weak order of a Coxeter system (W,S), inversion sets of elements of W and small roots. Small roots are the main ingredient introduced by Brink and Howlett in order to build a canonical automaton that recognizes the language of reduced words of elements of W over S. From small roots and inversion sets, we define a new finite class of elements in W called low elements. These low elements are the key to prove that the smallest subset of W containing S, closed under join (for the right weak order) and suffix is finite, and by ricochet that finitely generated Artin-Tits groups have a finite Garside family. Low elements seem rich in further applications in the study of infinite Coxeter groups, which will discuss if time allows.
(Based on joint works with Patrick Dehornoy and Matthew Dyer.)
You can add or remove yourself from a seminar mailing list by visiting this link.