Vidas Regelskis

Research

I am a mathematical physicist working in an area of mathematics called Representation Theory which, broadly speaking, seeks to understand complicated abstract algebraic structures, that are often inspired by physics, in terms of linear operators and their action on concrete linear spaces, which typically are Hilbert spaces of certain quantum systems.

I’m mostly interested in algebraic structures called Quantum Groups and Quantum Symmetric Pairs, examples of which are Yangians and twisted Yangians. These algebraic structures are certain deformations of classical objects, such like Lie groups and Lie algebras.

Representation theory of quantum groups is very different from that of classical objects. For instance, the category of finite dimensional representations of a simple Lie algebra is semi-simple, but this not the case for the Yangian of a simple Lie algebra: a monoidal product of two simple objects in the category is also a simple object, unless certain “shortening” conditions are met. This property gives rise to the so-called Functional Relations of Transfer Matrices in the theory of Quantum Integrable Models.

Other topics I’m interested-in include W-algebras, Yang-Baxter algebras, Integrable Spin Chains, Gaudin Models, Bethe Ansatz techniques, and more recently, Algebraic K-theory.