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Invariant distributions supported on the nilpotent cone of a semisimple Lie algebra

Author: Thierry Levasseur
Journal: Trans. Amer. Math. Soc. 353 (2001), 4189-4202
MSC (1991): Primary 14L30, 16S32, 17B20, 22E46
Published electronically: June 1, 2001
MathSciNet review: 1837227
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Abstract: Let $\mathfrak{g}$ be a semisimple complex Lie algebra with adjoint group $G$ and $\mathcal{D}(\mathfrak{g})$ be the algebra of differential operators with polynomial coefficients on $\mathfrak{g}$. If $\mathfrak{g}_0$ is a real form of $\mathfrak{g}$, we give the decomposition of the semisimple $ \mathcal{D}(\mathfrak{g})^G$-module of invariant distributions on $\mathfrak{g}_0$ supported on the nilpotent cone.

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Additional Information

Thierry Levasseur
Affiliation: Département de Mathématiques, Université de Brest, 29285 Brest, France

Keywords: Semisimple Lie algebra, invariant distribution, nilpotent orbit, Weyl group representation
Received by editor(s): November 17, 1998
Published electronically: June 1, 2001
Additional Notes: Research partially supported by EC TMR network “Algebraic Lie Representations”, Grant No. ERB FMRX-CT97-0100
Article copyright: © Copyright 2001 American Mathematical Society

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