Sugawara Construction for Higher Genus Riemann Surfaces

Schlichenmaier, Martin

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URN: urn:nbn:de:bsz:180-madoc-13257
Document Type: Working paper
Year of publication: 1998
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Abstract: By the classical genus zero Sugawara construction one obtains from admissible representations of affine Lie algebras (Kac-Moody algebras of affine type) representations of the Virasoro algebra. In this lecture first the classical construction is recalled. Then, after giving a review on the global multi-point algebras of Krichever-Novikov type for compact Riemann surfaces of arbitrary genus, the higher genus Sugawara construction is introduced. Finally, the lecture reports on results obtained in joint work with O.K. Sheinman. We were able to show that also in the higher genus, multi-point situation one obtains from representations of the global algebras of affine type representations of a centrally extended algebra of meromorphic vector fields on Riemann surfaces. The latter algebra is the generalization of the Virasoro algebra to higher genus.
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