|Speaker:||Francesco Sala (IPMU)|
|Title:||Continuum Kac-Moody Algebras and Continuum Quantum Groups|
|Date (JST):||Tue, Nov 19, 2019, 15:30 - 17:00|
|Place:||Seminar Room B|
The present talk is an account of a part of the research I have done during my 3 years at IPMU.
During the first part of the 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 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 using 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, Olivier Schiffmann, and Tatsuki Kuwagaki.