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- W2010990055 abstract "Let p be a parabolic subalgebra in a semisimple Lie algebra g . We study the module M p (λ) induced from a one-dimensional p -module of weight λ. Let U = U ( g )/ I be the quotient of the enveloping algebra U ( g ) by the annihilator I of the generic module induced from p . Let Z̃ denote the integral closure of the center Z of U , and Ũ = Z̃ U . Then M p (λ) is not only a U -module, but even a Ũ -module [ 1 ], so its central character Z → C extends to a central character Z̃ → C . We prove that this extended central character is useful: It is unique if and only if Dixmier's map is injective. Moreover, the “modified Dixmier-map” of the author's work (1998, Abh. Math. Sem. Univ. Hamburg 68 , 25–44) from the sheet S / G determined by p into the space X Ũ of minimal primitive ideals of Ũ is a homeomorphism S / G → X Ũ given by O ↦ Ann M p (λ). As an application, we obtain the following result related to Duflo's theorem that minimal primitive ideals are induced and centrally generated: Each minimal primitive ideal J of Ũ is induced and “almost” generated by its intersection m with the center, in the sense that J = m U ̃ . As further application of the main theorem we get results on the well-definedness of Dixmier's map." @default.
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- W2010990055 date "1999-03-01" @default.
- W2010990055 modified "2023-09-28" @default.
- W2010990055 title "Extended Central Characters and Dixmier's Map" @default.
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- W2010990055 doi "https://doi.org/10.1006/jabr.1998.7666" @default.
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