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Journal of Lie Theory 16 (2006), No. 3, 569--578
Copyright Heldermann Verlag 2006

Parabolic Induction of Projective Orbits and Subalgebras

Alexander V. Smirnov
Scientific Research Computing Center, Moscow State University, 119992 Moscow, Russia

The concepts of parabolic induction of subalgebras and varieties appeared independently in works of different authors. Here we introduce and study the parabolic induction of projective orbits. This concept turns out to be closely related to the above ones, and can be used as a method to study them. As an application, we describe all subalgebras of a semisimple Lie algebra that contain a given subalgebra obtained by parabolic induction.

Keywords: Representation theory, algebraic geometry, parabolic induction.

MSC: 20G05

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