Francesco Sala

Description

Title: Continuum Kac-Moody Lie algebras and continuum quantum groups

Abstract:
In the present talk, I will define a family of infinite-dimensional Lie algebras associated with a "continuum" analog of Kac--Moody Lie algebras. They depend on a "continuum" version of the notion of the quiver. These Lie algebras have some peculiar properties: for example, they do not have simple roots and in the
description of them in terms of generators and relations, only quadratic (!) Serre type relations appear.

I will discuss also their quantizations, called "continuum quantum groups". In particular, in the second part of the talk, I will focus on the case when the "continuum quiver" is a circle: in this case, the
continuum quantum group can be realized by means of the theory of classical Hall algebras. If time permits, I will discuss some preliminary results on the representation theory of the continuum
quantum group of the circle (in particular, the construction of the Fock space).

This is based on joint works with Andrea Appel and Olivier Schiffmann.

Period	9 Sept 2019
Visiting from	University of Tokyo, (Japan)
Visitor degree	PhD
Degree of Recognition	Local