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  Baxter Q-Operators and Representations of Yangians

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-CE86-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-CE88-3
Genre: Journal Article

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1010.3699 (Preprint), 422KB
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 Creators:
Bazhanov, Vladimir V., Author
Frassek, Rouven, Author
Lukowski, Tomasz, Author
Meneghelli, Carlo1, Author              
Staudacher, Matthias2, Author              
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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Free keywords: Mathematical Physics, math-ph, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,High Energy Physics - Theory, hep-th,Mathematics, Mathematical Physics, math.MP
 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.

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 Dates: 2010-10-182011
 Publication Status: Published in print
 Pages: 27 pages, 5 figures
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 Rev. Method: -
 Identifiers: arXiv: 1010.3699
DOI: 10.1016/j.nuclphysb.2011.04.006
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Title: Nuclear Physics B
Source Genre: Journal
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Publ. Info: Amsterdam : North-Holland
Pages: - Volume / Issue: 850 Sequence Number: - Start / End Page: 148 - 174 Identifier: ISSN: 0550-3213
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925564667