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

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

2006-12-02

arxiv.org/abs/nlin/0612003v1

SIGMA 2:084,2006

Nonlinear Sciences

Exactly Solvable and Integrable Systems

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2006.084

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.

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