Special Seminar

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