On the geometry of conjugacy classes in classical groups |
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Authors: | Hanspeter Kraft Claudio Procesi |
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Institution: | 1. Mathematisches Institut Universit?t Basel, Rheinsprung 21, CH-4051, Basel 2. Instituto Matematico Guido Castelnuovo, Università di Roma, I-00100, Roma
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Abstract: | 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.
Supported in part by the SFB Theoretische Mathematik, University of Bonn, and by the University of Hamburg |
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