Abstract:
We speak about the part of integrable system theory dealing with conformal theory and W-algebras (ordinary and deformed). Some new approaches to finding Bethe equations that describe the spectrum of Hamiltonians of these quantum integrable systems are developed. The derivation of the Bethe equations is based on the technique of shuffle algebras arising in quantum group theory.
Key words and phrases:
integrable system, shuffle algebra, Bethe equations, affine Lie algebra, center at the critical level, Drinfeld–Sokolov reduction, quantum group.