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SIGMA 2 (2006), 084, 20 pages nlin.SI/0612003
https://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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