\(\mathcal R\)-matrix and Baxter \(\mathcal Q\)-operators for the noncompact \(\mathrm{SL}(N,\mathbb C)\) invariant spin chain
In this article, one constructs the \(\text{SL}(N,\mathbb C)\) invariant \(R\)-operator which acts on the tensor product of two principal series representations of the \(\text{SL}(N,\mathbb C)\) group. The \(R\)-operator is obtained in the form of the product of elementary operators \(U_{k}, k=1,\dots,2N-1\), which satisfy commutation relations similar to those of the operators of the standard permutation. This result has direct application to the Baxter operators, and provides a simple proof of the Yang-Baxter relation.
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