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A Garside presentation for Artin-Tits groups of type C ˜ n

F. Digne (2012)

Annales de l’institut Fourier

We prove that an Artin-Tits group of type C ˜ 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 “generated group” 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 ˜ , and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...

A Lagrangian representation of tangles II

David Cimasoni, Vladimir Turaev (2006)

Fundamenta Mathematicae

The present paper is a continuation of our previous paper [Topology 44 (2005), 747-767], where we extended the Burau representation to oriented tangles. We now study further properties of this construction.

About presentations of braid groups and their generalizations

V. V. Vershinin (2014)

Banach Center Publications

In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard Artin presentation for generalizations of braids. Namely, we consider presentations with small number of generators, Sergiescu graph-presentations and Birman-Ko-Lee presentation. The work of V.~V.~Chaynikov on the word and conjugacy problems for the singular...

Affine braid group actions on derived categories of Springer resolutions

Roman Bezrukavnikov, Simon Riche (2012)

Annales scientifiques de l'École Normale Supérieure

In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...

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