On some new constructions in quantum vertex algebra theory

Abstract: One important problem in the vertex algebra theory is to associate certain vertex algebra-like objects, the quantum vertex algebras, to various classes of quantum groups, such as quantum affine algebras or double Yangians. In this talk, after giving a brief introduction to the main concepts of quantum vertex algebra theory, I will discuss the aforementioned problem in the setting of the Etingof-Kazhdan quantum affine vertex algebra associated with the trigonometric R-matrix of type A. The main focus will be on its connection with the representation theory of the quantum affine algebra of type A, the explicit description of its center at the critical level and some further applications to the construction of certain commutative subalgebras. The talk is in part based on the joint works with Lucia Bagnoli and Alexander Molev.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.