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

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.

arXiv commentThis 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 http://www.emis.de/journals/SIGMA/

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