Baxter Q-Operators and Representations of Yangians

Details Baxter Q-Operators and Representations of Yangians Baxter Q-Operators and Representations of Yangians

2010-10-18

arxiv.org/abs/1010.3699v2

Nucl.Phys.B850:148-174,2011

Physics

Mathematical Physics

27 pages, 5 figures; v2: typos fixed, references updated and added

Scientific paper

10.1016/j.nuclphysb.2011.04.006

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.

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