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International Mathematics Research Papers (2006) Vol. 2006 : article ID 96895, 71 pages, doi:10.1155/IMRP/2006/96895
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Shapovalov determinants of Q-type Lie superalgebras

Maria Gorelik

Department of Mathematics, Incumbent of the Frances and Max Hersh Career Development Chair, The Weizmann Institute of Science Rehovot 76100, Israel E-mail address: maria.gorelik{at}weizmann.ac.il

We define an analogue of Shapovalov forms for Q-type Lie superalgebras and factorize the corresponding Shapovalov determinants which are responsible for simplicity of the highest weight modules. We apply the factorization to obtain a description of the centres of Q-type Lie superalgebras.


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