Baxter Q-Operators and Representations of Yangians

Vladimir V. Bazhanov, Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

MSC 2000

16W30 Coalgebras, bialgebras, Hopf algebras ; rings, modules, etc. on which these act

82B23 Exactly solvable models; Bethe ansatz

Abstract
We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider sl(n) compact spin chains and derive the full hierarchy of operatorial functional equations for all related commuting transfer matrices and Q-operators. This leads to a systematic and transparent solution of these chains, where the nested Bethe equations are derived in an entirely algebraic fashion, without any reference to the traditional Bethe ansatz techniques.