Commuting differential and difference operators associated to complex curves, II

Details Commuting differential and difference operators associated to complex curves, II Commuting differential and difference operators associated to complex curves, II

1998-12-28

arxiv.org/abs/math/9812152v1

Mathematics

Quantum Algebra

Scientific paper

We construct a commuting family of difference-evaluation operators, deforming the commuting family introduced in our earlier paper (math/9807145). We interpret them as the action of the center of quantum algebras in the space of intertwiners for a ``regular'' subalgebra. These algebras are the quantum groups associated with sl_2 and algebraic curves, introduced by V. Rubtsov and the first author (q-alg/9608005). In the case of rational curves, our operators coincide those provided by the Yangian action on the hypergeometric spaces of Tarasov and Varchenko (q-alg/9604011).

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