Differential Operator Algebras on compact Riemann Surfaces

Details Differential Operator Algebras on compact Riemann Surfaces Differential Operator Algebras on compact Riemann Surfaces

1993-11-05

arxiv.org/abs/hep-th/9311036v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, AmsTeX 2.1 and psbox macros

Scientific paper

Invited talk at the International Symposium on Generalized Symmetries in Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July 29, 1993. This talk reviews results on the structure of algebras consisting of meromorphic differential operators which are holomorphic outside a finite set of points on compact Riemann surfaces. For each partition into two disjoint subsets of the set of points where poles are allowed, a grading of the algebra and of the modules of lambda - forms is introduced. With respect to this grading the Lie structure of the algebra and of the modules are almost graded ones. Central extensions and semi-infinite wedge representations are studied. If one considers only differential operators of degree 1 then these algebras are generalizations of the Virasoro algebra in genus zero, resp. of Krichever Novikov algebras in higher genus.

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