Orbites Nilpotentes Sphériques et Représentations unipotentes associées: Le cas 𝑆𝐿_𝑛

Sabourin, Hervé

doi:10.1090/S1088-4165-05-00196-2

Orbites Nilpotentes Sphériques et Représentations unipotentes associées: Le cas $\bf SL{\textunderscore }n$
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by Hervé Sabourin

Represent. Theory 9 (2005), 468-506

DOI: https://doi.org/10.1090/S1088-4165-05-00196-2

Published electronically: August 11, 2005

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Abstract:

Let $G$ be a real simple Lie group and $\mathfrak {g}$ its Lie algebra. Given a nilpotent adjoint $G$-orbit $O$, the question is to determine the irreducible unitary representations of $G$ that we can associate to $O$, according to the orbit method. P. Torasso gave a method to solve this problem if $O$ is minimal. In this paper, we study the case where $O$ is any spherical nilpotent orbit of $sl_n({\mathbb R})$, we construct, from $O$, a family of representations of the two-sheeted covering of $SL_n({\mathbb R})$ with Torasso’s method and, finally, we show that all these representations are associated to the corresponding orbit.

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