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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0612003 (nlin)
[Submitted on 2 Dec 2006]

Title:R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

Authors:Sergey E. Derkachov, Alexander N. Manashov
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Abstract: The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to the Yang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) for arbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtained in an explicit form. We construct the commutative family of the operators $\mathcal{Q}_k(u)$ which can be identified with the Baxter operators for the noncompact $SL(N,\mathbb{C})$ spin magnet.
Comments: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at this http URL
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA)
Cite as: arXiv:nlin/0612003 [nlin.SI]
  (or arXiv:nlin/0612003v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0612003
Journal reference: SIGMA 2:084,2006
Related DOI: https://doi.org/10.3842/SIGMA.2006.084

Submission history

From: Sergey E. Derkachov [view email] [via SIGMA proxy]
[v1] Sat, 2 Dec 2006 15:20:24 UTC (26 KB)
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