Some examples of quantum groups in higher genus
Abstract
This is a survey of our construction of current algebras, associated with complex curves and rational differentials. We also study in detail two classes of examples. The first is the case of a rational curve with differentials zn dz; these algebras are ``building blocks'' for the quantum current algebras introduced in our earlier work. The second is the case of a genus >1 curve X, endowed with a regular differential having only double zeroes.
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