Artin groups, symmetries, and linear representations
speaker: Luis Paris (Université de Bourgogne)abstract: The talk is based on a join work with Olivier Geneste. One of the most popular questions on braid groups has been for a long time whether these groups are linear. This question was solved in the late 90s by Bigelow and Krammer. Krammer's construction was then extended to all simply laced Artin groups of spherical type by Cohen--Wales and Digne, and, afterwards, to all simply laced Artin groups without triangles by myself. Now, we would like to extend the construction to the other Artin groups, or, at least, to some Artin groups that are not simply laced. An answer partially lies in some works by Digne and Castella that, in particular, provide such a construction for the Artin groups of type $Bn$, $F4$, and $G2$, by means of symmetries of Coxeter graphs. We will explain this story in more detail, show how Digne's ideas can be extended to other Artin groups, and what are the limits of such a construction.
timetable:
Thu 8 Jun, 11:40 - 12:20, Aula Dini
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