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arXiv · 1801.06909

Admissible modules and normality of classical nilpotent orbits I

Dan Barbasch·Kayue Daniel Wong
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Abstract

In the case of complex symplectic and orthogonal groups, we find $(\mathfrak{g}, K)-$modules with the property that their $K-$structure matches the structure of regular functions on the closures of nilpotent orbits. This establishes a version of the Orbit Method of Kirrilov-Kostant-Souriau as proposed by Vogan. In the process we give another proof of the classification of nilpotent orbits with normal closure in the Lie algebra of a classical group first established by Kraft-Procesi.

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Dan Barbasch, Kayue Daniel Wong. 2018-01-21. Admissible modules and normality of classical nilpotent orbits I. https://arxiv.org/abs/1801.06909

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