Quantum Groups and Representation Theory

Staff: Dr Vidas Regelskis, Dr Charles Young

A model of a physical system (classical or quantum-mechanical) is said to be integrable if it possesses enough symmetries to enable it to be, in some suitable sense, exactly solved. These additional symmetries are typically hidden in some way, and their study has led to the discovery of new algebraic structures, in a broad sense, called quantum groups. Representation theory allows us to better understand quantum groups by realising them concretely using matrices or linear maps and studying transformations of the associated spaces.

Our work in this area concerns:

  • Kac-Moody Lie algebras and their deformations
  • R-matrices and the Yang-Baxter equation
  • W-algebras