91. 14/10/2024 Slaven Kožić (University of Zagreb, Croatia)

Title: Representations of the quantum affine vertex algebra associated with the trigonometric R-matrix of A
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, I will discuss this problem in the context of Etingof--Kazhdan's quantum affine vertex algebra V^c(gl_N) associated with the trigonometric R-matrix of type A. The main focus will be on the explicit description of the center of V^c(gl_N) at the critical level c=-N and, furthermore, on the connection between certain classes of V^c(gl_N)-modules and representation theories of the quantum affine algebra of type A and the orthogonal twisted h-Yangian. The talk is in part based on the joint works with Alexander Molev and Lucia Bagnoli.
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