Orbites Nilpotentes Sphériques et Représentations unipotentes associées : Le cas $SL_n$

Details Orbites Nilpotentes Sphériques et Représentations unipotentes associées : Le cas $SL_n$ Orbites Nilpotentes Sphériques et Représentations unipotentes associées : Le cas $SL_n$

2004-07-22

arxiv.org/abs/math/0407376v1

Mathematics

Representation Theory

Scientific paper

Let $G$ be a real simple Lie group, $\got g$ 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, in [22], 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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