David Bessis

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We describe a new monoid structure for braid groups associated with finite Coxeter systems. This monoid shares with the classical positive braid monoid its crucial algebraic properties: the monoid satisfies Öre’s conditions and embeds in its group of fractions, it admits a nice normal form, it can be used to construct braid group actions on categories... It(More)
Springer theory of regular elements (introduced in [Sp]) explains how certain complex reflection groups naturally arise as centralizers in other complex reflection groups of particular elements, the regular elements. The construction relies on invariant theory and elementary algebraic geometry, and gives precise information on the relation between the two(More)
Let V be a finite dimensional complex vector space and W ⊆ GL(V ) be a finite complex reflection group. Let V reg be the complement in V of the reflecting hyperplanes. We prove that V reg is a K(π, 1) space. This was predicted by a classical conjecture, originally stated by Brieskorn for complexified real reflection groups. The complexified real case(More)
To any complex reflection group W ⊂ GL(V ), one may attach a braid group B(W ), defined as the fundamental group of the space of regular orbits for the action of W on V [Broué et al. 98]. The “ordinary” braid group on n strings, introduced by [Artin 47], corresponds to the case of the symmetric group Sn, in its monomial reflection representation in GLn(C).(More)
Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Broué-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is(More)
Finite subgroups of GLn(Q) generated by reflections, known as Weyl groups, classify simple complex Lie Groups as well as simple algebraic groups. They are also building stones for many other significant mathematical objects like braid groups and Hecke algebras. Through recent work on representations of reductive groups over finite fields based upon George(More)
We construct a quasi-Garside monoid structure for the free group. This monoid should be thought of as a dual braid monoid for the free group, generalising the constructions by Birman-Ko-Lee and by the author of new Garside monoids for Artin groups of spherical type. Conjecturally, an analog construction should be available for arbitrary Artin groups and for(More)