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Journal of Lie Theory 16 (2006), No. 1, 155--219
Copyright Heldermann Verlag 2006

Minimal Polynomials and Annihilators of Generalized Verma Modules of the Scalar Type

Hiroshi Oda
Faculty of Engineering, Takushoku University, 815-1 Tatemachi, Hachioji-shi, Tokyo 193-0985, Japan

Toshio Oshima
Grad. School Math. Sciences, University of Tokyo, 7-3-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

We construct a generator system of the annihilator of a generalized Verma module of a reductive Lie algebra induced from a character of a parabolic subalgebra as an analogue of the minimal polynomial of a matrix.

Keywords: Generalized Verma modules, minimal polynomials, Harish-Chandra homomorphisms.

MSC: 22E47, 16S30

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