Baxter QOperators and Representations of Yangians
Vladimir V. Bazhanov
Bazhanov
Vladimir V.
Rouven Frassek
Frassek
Rouven
Tomasz Lukowski
Lukowski
Tomasz
Carlo Meneghelli
Meneghelli
Carlo
Matthias Staudacher
Staudacher
Matthias
Baxter QOperators 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 Qoperators 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 YangBaxter equation connected with harmonic oscillator algebras. These infinitestate solutions of the YangBaxter 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 Qoperators. 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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