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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm014, 28 pages, doi:10.1093/imrn/rnm014 published on May 24, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

On a Generic Verma Module at the Critical Level Over Affine Lie Superalgebras

Maria Gorelik

Weizmann Institute of Science, PO Box 26, Rehovot 76100, Israel

Correspondence: Correspondence to be sent to: Maria Gorelik, The Incumbent of te Frances andMax Hersh Career Development Chair, Weizmann Institute of Science, PO Box 26, Rehovot 76100, Israel. e-mail: maria.gorelik{at}weizmann.ac.il

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra g != A(2k, 2l)(4). We obtain the character formula for a simple module with a generic highest weight at the critical level conjectured by V. G. Kac and D. A. Kazhdan.

Communicated by Edward Frenkel


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