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

Levasseur, Thierry

doi:10.1090/S0002-9947-01-02851-3

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

Trans. Amer. Math. Soc. 353 (2001), 4189-4202

DOI: https://doi.org/10.1090/S0002-9947-01-02851-3

Published electronically: June 1, 2001

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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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