Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 084, 20 pages      nlin.SI/0612003      http://dx.doi.org/10.3842/SIGMA.2006.084
Contribution to the Vadim Kuznetsov Memorial Issue

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

Sergey É. Derkachov a and Alexander N. Manashov b, c
a) St.-Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, 191023 St.-Petersburg, Russia
b) Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany
c) Department of Theoretical Physics, Sankt-Petersburg University, St.-Petersburg, Russia

Received October 30, 2006; Published online December 02, 2006

Abstract
The problem of constructing the SL(N,C) invariant solutions to the Yang-Baxter equation is considered. The solutions (R-operators) for arbitrarily principal series representations of SL(N,C) are obtained in an explicit form. We construct the commutative family of the operators Qk(u) which can be identified with the Baxter operators for the noncompact SL(N,C) spin magnet.

Key words: Yang-Baxter equation; Baxter operator.

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