Baxter Q-Operators and Representations of Yangians
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.
Cite
@article{arxiv.1010.3699,
title = {Baxter Q-Operators and Representations of Yangians},
author = {Vladimir V. Bazhanov and Rouven Frassek and Tomasz Lukowski and Carlo Meneghelli and Matthias Staudacher},
journal= {arXiv preprint arXiv:1010.3699},
year = {2011}
}
Comments
27 pages, 5 figures; v2: typos fixed, references updated and added