Martin Schlichenmaier
Differential Operator Algebras on compact Riemann Surfaces, 11 pages,
AmsTeX 2.1 and psbox macros, Mannheimer Manuskripte 164
(53K, AMSTEX)
ABSTRACT. 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.
(to appear in the Proceedings)