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On the geometry of conjugacy classes in classical groups

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Commentarii Mathematici Helvetici

Summary

We study closures of conjugacy classes in the Lie algebras of the orthogonal and symplectic groups and determine which ones are normal varieties. Furthermore we give a complete classification of the minimal singularities which arise in this context, i.e. the singularities which occur in the open classes in the boundary of a given conjugacy class. In contrast to the results for the general linear group ([KP1], [KP2]) there are classes with non normal closure; they are branched in a class of codimension two and give rise to normal minimal singularities. The methods used are (classical) invariant theory and algebraic geometry.

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Authors and Affiliations

  1. Mathematisches Institut Universität Basel, Rheinsprung 21, CH-4051, Basel

    Hanspeter Kraft & Claudio Procesi

  2. Instituto Matematico Guido Castelnuovo, Università di Roma, I-00100, Roma

    Hanspeter Kraft & Claudio Procesi

Authors
  1. Hanspeter Kraft
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  2. Claudio Procesi
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Supported in part by the SFB Theoretische Mathematik, University of Bonn, and by the University of Hamburg

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Kraft, H., Procesi, C. On the geometry of conjugacy classes in classical groups. Commentarii Mathematici Helvetici 57, 539–602 (1982). https://doi.org/10.1007/BF02565876

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  • DOI: https://doi.org/10.1007/BF02565876

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