A GARSIDE PRESENTATION FOR ARTIN-TITS GROUPS OF TYPE (C)over-tilde(n)

作者：Digne F^*

来源：Annales de l'Institut Fourier, 2012, 62(2): 641-666.

DOI：10.5802/aif.2690

• Braids
• Garside
• Artin-Tits groups
• affine Coxeter groups

We prove that an Artin-Tits group of type (C) over tilde is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the %26quot;generated group%26quot; method. This answers, in this particular case, a general question on Artin-Tits groups, gives a new presentation of an Artin-Tits group of type (C) over tilde, and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof is to show that this group is a group of fixed points in an Artin-Tits group of type (A) over tilde under an involution. Another important point is the study of the Hurwitz action of the usual braid group on the decomposition of a Coxeter element into a product of reflections.

• 出版日期2012