Traces of Intertwining Operators for the Yangian Double

The traces over infinite dimensional representations of the central extended Yangian double for the product of operators which intertwine these representations are calculated. For the special combinations of the intertwining operators the traces are identified with form factors of local operators in SU(2)-invariant Thirring model. This identification is based on the identities which are deformed analogs of the Gauss-Manin connection identities for the hyperelliptic curves.