Extended affine Weyl groups and twist automorphisms
Organizer
Speaker
Takumi Otani
Time
Tuesday, September 24, 2024 12:30 PM - 1:30 PM
Venue
A3-2a-302
Abstract
Dubrovin-Zhang introduced the extended affine Weyl groups for affine root systems in the study of Frobenius manifolds.
However, it was unknown how to construct the extended affine Weyl groups in terms of root systems.
In this talk, we define the twist automorphism for a generalized root system of affine ADE type and show that the extended affine Weyl group is induced by the twist automorphism.
Moreover, we prove that there exists a biholomorphism between the Dubrovin-Zhang’s orbit space and the orbit space of the universal covering space of a certain subspace of the Cartan subalgebra.
If time permits, we explain the one-to-one correspondence between the set of certain root bases modulo twist automorphisms and the set of full exceptional collections modulo spherical twists.