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- W1969896886 abstract "0.1. Let g be a semisimple Lie algebra with Cartan subalgebra h , Weyl Ž . group W, and enveloping algebra U g . Several results illustrate the Ž . Ž . important role played by the center Z g of U g . First there is the Ž . Harish-Chandra homomorphism which shows that Spec Z g ( h*rW, Ž . and describes the action of Z g on highest weight modules. Next we w x recall the separation of variables Theorem of Kostant Ko; D, 8.2.4 which Ž . states that there is an ad g-invariant subspace K of U g such that the Ž . Ž . multiplication map K m Z g a U g is an isomorphism of ad g-modules. w Kostant’s theorem is a key ingredient in the proof of a result of Duflo D, x 8.4.3 stating that the annihilator of a Verma module is generated by its Ž . intersection with Z g . A version of the Harish-Chandra homomorphism has been given by Kac for basic classical simple Lie superalgebras. We recall the details in Subsection 1.1. The proof of Kostant’s theorem depends heavily on the fact that every finite dimensional g-module is completely reducible. By contrast if g is a simple Lie superalgebra, such that every finite dimensional g-module is completely reducible, then either g is a simple Lie algebra or g is an Ž . w orthosymplectic Lie superalgebra g s osp 1, 2 r for some r G 1 Sch, x Theorem 1, p. 239 . Ž . Ž . In this paper we show that for g s osp 1, 2 r we again have U g ( Ž . K m Z g for K ad-invariant. In addition if E is any finite dimensional" @default.
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- W1969896886 date "1997-07-01" @default.
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- W1969896886 title "On the Center of the Enveloping Algebra of a Classical Simple Lie Superalgebra" @default.
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- W1969896886 doi "https://doi.org/10.1006/jabr.1996.7000" @default.
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