| Speaker: | Kyoji Saito(IPMU) |
|---|---|
| Title: | Elliptic Artin groups I |
| Date (JST): | Sat, Mar 30, 2019, 10:00 - 17:00 |
| Place: | Balcony A |
| Abstract: |
Artin groups (called also generalized braid groups by Deligne) appear as fundamental groups of regular orbit spaces of the classical Weyl groups, and are presented by Artin braid relations associated with the Coxeter-Dynkin diagram. They play basic roles both in geometry and representation theory. According to the generalization of the classical root systems to elliptic root systems, we introduce and investigate elliptic Artin groups. Similar to the Artin group, they first appear as the fundamental groups of regular orbit spaces of elliptic Weyl group actions. Then, they are presented by a generalization of Artin braid relations defined on elliptic diagrams. In the study group, we shall explain in down-to-earth terms without assuming any prior knowledge of elliptic root systems. One of the most crucial differences of Elliptic Artin groups from the classical Artin groups is that they admit an action of the central extensions of elliptic modular groups: $\Gamma_0(1), \Gamma_0(2)$ or $\Gamma_0(3)$. This fact is based on the fact that the rank 2 radical of an elliptic root system is geometrically identified with the homology group of an elliptic curve of 1, 2 or 3 marked points. These three cases correspond to the classical Weierstrass, Legendre and Hesse family of elliptic curves, respectively. Organizer: Kyoji Saito(kyoji.saito@ipmu.jp) |
| Remarks: | Blackboard talk |
