Sugawara Construction and Casimir Operators for Krichever-Novikov Algebras

Schlichenmaier, Martin ; Sheinman, Oleg K.

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URN: urn:nbn:de:bsz:180-madoc-13208
Document Type: Working paper
Year of publication: 1995
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
Subject headings (SWD): Virasoro-Algebra , Kac-Moody-Algebra , Casimir-Operator , Krichever-Novikov-Algebra
Abstract: We show how to obtain from highest weight representations of Krichever-Novikov algebras of affine type (also called higher genus affine Kac-Moody algebras) representations of centrally extended Krichever-Novikov vector field algebras via the Sugawara construction. This generalizes classical results where one obtains representations of the Virasoro algebra. Relations between the weights of the corresponding representations are given and Casimir operators are constructed. In an appendix the Sugawara construction for the multi-point situation is done.

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