|Speaker:||Todor Eliseev Milanov (Kavli IPMU)|
|Title:||Affine Artin groups|
|Date (JST):||Thu, Sep 12, 2013, 15:30 - 17:00|
|Place:||Seminar Room A|
An affine Artin groups is by definition the fundamental group of the space of regular orbits of the corresponding affine Weyl group. My main goal is to explain how one can compute the fundamental groups via chamber theory. This approach to the affine Artin group is based on ideas of Deligne and it was developed by Van der Lek.
My interest in the above problem is related to the string lunch talk that I gave recently. Namely, I introduced a certain set of vertex operators that are multivalued analytic functions on the Riemann sphere. It is interesting to study the commutation relations of the vertex operators near their singularities. In particular, near infinity we can recover the basic representation of an affine Lie algebra. It turns out that, in some sense, one can analytically decompose the representation into simpler ones via analytical continuation to the remaining singular points. This is precisely the place where the affine Artin group plays a crucial role. Most of these vertex algebra constructions are still work in progress, so I will talk about them very briefly and concentrate mostly on the affine Artin group.