A study of representation theory of toroidal quantum groups

Project title: A study of representation theory of toroidal quantum groups

Project No. 09.3.3.-LMT-K-712-21-0077

This project has received funding from the European Social Fund under the No. 09.3.3-LMT-K-712 “Development of Competences of Scientists, other Researchers and Students through Practical Research Activities” measure under grant agreement with the Research Council of Lithuania (LMTLT).

Duration: from 2020-10-09 to 2021-03-17

Participant: dr. Vidas Regelskis

Summary: Quantum groups form a wide family of noncommutative associative algebras closely linked to strongly interacting quantum and classical dynamical systems. Toroidal quantum groups are obtained by quantising doubly-affinised simple Lie algebras. The goal of this project is to advance the highest weight representation theory of toroidal quantum groups known by the name of affine Yangians, and find evaluation modules associated with the Yang-Baxter equation and the problem of quantising the Kadomtsev–Petviashvili equation describing nonlinear wave motion is shallow water.