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The normality of closures of orbits in a Lie algebra

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Commentarii Mathematici Helvetici

Abstract

LexX be the closure of aG-orbit in the Lie algebra of a connected reductive groupG. It seems that the varietyX is always normal. After a reduction to nilpotent orbits, this is proved for some special cases. Results on determinantal schemes are used forGl n . IfX is small enough we use a resolution and Bott's theorem on the cohomology of homogeneous vector bundles. Our results are conclusive for groups of typeA 1,A 2,A 3 andB 2.

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Authors and Affiliations

  1. Hoogbouw WSN, Mathematisch Instituut, Post box 800, Groningen, Netherlands

    Wim Hesselink

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Hesselink, W. The normality of closures of orbits in a Lie algebra. Commentarii Mathematici Helvetici 54, 105–110 (1979). https://doi.org/10.1007/BF02566258

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