Geodesic
Zamolodchikov–Faddeev algebras for Yangian doubles at level 1
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 1, pp. 25-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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The representation theory of centrally extended Yangian doubles is investigated. The intertwining operators are constructed for infinite dimensional representations of $\widehat{DY(\mathfrak{sl}_2)}$, which are deformed analogs of the highest weight representations of the affine algebra $\widehat{\mathfrak{sl}}_2$ at level 1. We give bosonized expressions for the intertwining operators and verify that they generate an algebra isomorphic to the Zamolodchikov–Faddeev algebra for the $SU(2)$-invariant Thirring model. From them, we compose $L$-operators by Miki's method and verify that they coincide with $L$-operators constructed from the universal $\mathcal R$-matrix. The matrix elements of the product of these operators are calculated explicitly and are shown to satisfy the quantum (deformed) Knizhnik–Zamolodchikov equation associated with the universal $\mathcal R$-matrix for $\widehat{DY(\mathfrak{sl}_2)}$. 
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     author = {D. R. Lebedev and S. Z. Pakulyak and S. M. Khoroshkin},
     title = {Zamolodchikov{\textendash}Faddeev algebras for {Yangian} doubles at level~1},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {25--45},
     year = {1997},
     volume = {110},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_110_1_a2/}
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D. R. Lebedev; S. Z. Pakulyak; S. M. Khoroshkin. Zamolodchikov–Faddeev algebras for Yangian doubles at level 1. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 1, pp. 25-45. http://geodesic.mathdoc.fr/item/TMF_1997_110_1_a2/

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