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Journal Article

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

##### MPS-Authors

##### Locator

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##### Fulltext (public)

1010.3699

(Preprint), 422KB

NPB850_148.pdf

(Any fulltext), 453KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Bazhanov, V. V., Frassek, R., Lukowski, T., Meneghelli, C., & Staudacher, M. (2011).
Baxter Q-Operators and Representations of Yangians.* Nuclear Physics B,* *850*,
148-174. doi:10.1016/j.nuclphysb.2011.04.006.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-CE86-7

##### 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.