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The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to theYang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) forarbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtainedin an explicit form. We construct the commutative family of the operators$\mathcal{Q}_k(u)$ which can be identified with the Baxter operators for thenoncompact $SL(N,\mathbb{C})$ spin magnet.

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