Geodesic
Quantum Volterra model and universal $R$-matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 3, pp. 384-396

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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. 
@article{TMF_1997_113_3_a2,
     author = {A. V. Antonov},
     title = {Quantum {Volterra} model and universal $R$-matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {384--396},
     publisher = {mathdoc},
     volume = {113},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_3_a2/}
}
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A. V. Antonov. Quantum Volterra model and universal $R$-matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 3, pp. 384-396. http://geodesic.mathdoc.fr/item/TMF_1997_113_3_a2/