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Mathematical Physics

arXiv:1411.7595 (math-ph)
[Submitted on 27 Nov 2014 (v1), last revised 11 Mar 2016 (this version, v4)]

Title:From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation

Authors:Dmitry Chicherin, Sergey E. Derkachov, Vyacheslav P. Spiridonov
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Abstract:We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group $\mathrm{SL}(2,\mathbb{C})$ or Faddeev's modular double. Then we describe its restriction to an irreducible finite-dimensional representation in one or both spaces. In this way we obtain very simple explicit formulas embracing rational and trigonometric finite-dimensional solutions of the Yang-Baxter equation. Finally, we construct these finite-dimensional solutions by means of the fusion procedure and find a nice agreement between two approaches.
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)
Cite as: arXiv:1411.7595 [math-ph]
  (or arXiv:1411.7595v4 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1411.7595
Journal reference: SIGMA 12 (2016), 028
Related DOI: https://doi.org/10.3842/SIGMA.2016.028

Submission history

From: Dmitry Chicherin [view email] [via SIGMA proxy]
[v1] Thu, 27 Nov 2014 13:43:55 UTC (41 KB)
[v2] Wed, 18 Mar 2015 12:09:16 UTC (41 KB)
[v3] Sun, 15 Nov 2015 21:16:25 UTC (42 KB)
[v4] Fri, 11 Mar 2016 05:24:16 UTC (44 KB)
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