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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Invariant distributions supported on the nilpotent cone of a semisimple Lie algebra
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by Thierry Levasseur PDF
Trans. Amer. Math. Soc. 353 (2001), 4189-4202 Request permission

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
  • Email: Thierry.Levasseur@univ-brest.fr
  • 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
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 4189-4202
  • MSC (1991): Primary 14L30, 16S32, 17B20, 22E46
  • DOI: https://doi.org/10.1090/S0002-9947-01-02851-3
  • MathSciNet review: 1837227