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Mathematics > Quantum Algebra

arXiv:1408.3364 (math)
[Submitted on 14 Aug 2014 (v1), last revised 15 Jul 2015 (this version, v3)]

Title:Boundary transfer matrices and boundary quantum KZ equations

Authors:Bart Vlaar
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Abstract:A simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin's boundary transfer matrices by merely imposing appropriate reflection equations, i.e. without using the conditions of crossing symmetry and unitarity of the R-matrix.
Comments: 26 pages; 2 figures; strengthening of results in Section 2; small modifications (corrected typos etc.) throughout; updated Acknowledgments
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph)
Cite as: arXiv:1408.3364 [math.QA]
  (or arXiv:1408.3364v3 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.1408.3364
Journal reference: J. Math. Phys. 56, 071705 (2015)
Related DOI: https://doi.org/10.1063/1.4927305

Submission history

From: Bart Vlaar [view email]
[v1] Thu, 14 Aug 2014 17:46:58 UTC (32 KB)
[v2] Fri, 31 Oct 2014 19:34:24 UTC (30 KB)
[v3] Wed, 15 Jul 2015 17:52:02 UTC (126 KB)
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