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Traces of intertwining operators for the Yangian double. (English) Zbl 0973.17022

Summary: 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 the 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.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T10 Model quantum field theories
82B23 Exactly solvable models; Bethe ansatz
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