Abstract:
In this paper, we explicitly prove that an integrable system solved by the quantum inverse scattering method can be described by a pure algebraic object (universal $R$-matrix) and a proper algebraic representation. For the example of the quantum Volterra model, we construct the $L$-operator and the fundamental $R$-matrix from the universal $R$-matrix for the quantum affine $U_q(\widehat{sl}_2)$ algebra and $q$-oscillator representation for it. In this way, there is an equivalence between the integrable system with the symmetry algebra $\mathcal A$ and the representation of this algebra.
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