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Baxter Q-operators and representations of Yangians

Baxter Q-operators and representations of Yangians,10.1016/j.nuclphysb.2011.04.006,Nuclear Physics B,Vladimir V. Bazhanov,Rouven Frassek,Tomasz Łukows

Baxter Q-operators and representations of Yangians  
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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 gl(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.
Journal: Nuclear Physics B - NUCL PHYS B , vol. 850, no. 1, pp. 148-174, 2011
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