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Complexity and nilpotent orbits

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Abstract

New formulas for the complexity and the rank of an arbitrary homogeneous space of a reductive group are given. These completely reduce the problem to finding of stabilizers of general position in linear representations of reductive groups. As an application a description of spherical (i.e. of complexity zero) nilpotent orbits is obtained and it is proved that the complexity and the rank of orbits are constant along the sheets of the adjoint representation.

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  1. Moscow Radioelectronics and Automation Institute, Prosp. Vernadskogo, 78, 117454, Moscow, Russia

    Dmitrii I. Panyushev

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  1. Dmitrii I. Panyushev
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Panyushev, D.I. Complexity and nilpotent orbits. Manuscripta Math 83, 223–237 (1994). https://doi.org/10.1007/BF02567611

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  • DOI: https://doi.org/10.1007/BF02567611

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