Zamolodchikov-Faddeev algebras for Yangian doubles at level 1 (Q1280817)

Various representations and intertwining operators of the central extension \( \widehat{\text{DY}( {\mathfrak sl}_{2}) }\) of the quantum double \(\text{DY}( {\mathfrak sl}_{2}) \) are constructed and studied in application to continuous integrable quantum field theories. The bosonized expressions for the intertwining operators are given and coincidence of \(L\)-operators is obtained by Miki's method and the ones constructed from the universal \({\mathcal R}\)-matrix is proved. The matrix elements of \(L\)-operator products are derived explicitly and it is shown that they satisfy the deformed Knizhnik-Zamolodchikov equation which is associated with the universal \( {\mathcal R}\)-matrix for \(\widehat{\text{DY}( {\mathfrak sl}_{2}) }\).