On the geometry of conjugacy classes in classical groups View Full Text


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Article Info

DATE

1982-12

AUTHORS

Hanspeter Kraft, Claudio Procesi

ABSTRACT

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. More... »

PAGES

539-602

References to SciGraph publications

  • 1979-12. The normality of closures of orbits in a Lie algebra in COMMENTARII MATHEMATICI HELVETICI
  • 1976-10. On the collapsing of homogeneous bundles in INVENTIONES MATHEMATICAE
  • 1970-12. Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen in INVENTIONES MATHEMATICAE
  • 1978-10. Parametrisierung von Konjugationsklassen in in MATHEMATISCHE ANNALEN
  • 1979-10. Closures of conjugacy classes of matrices are normal in INVENTIONES MATHEMATICAE
  • 1973. Toroidal Embeddings I in NONE
  • 1980. Simple Singularities and Simple Algebraic Groups in NONE
  • 1976-10. Cohomology and the resolution of the nilpotent variety in MATHEMATISCHE ANNALEN
  • 1980-10. Minimal singularities inGLn in INVENTIONES MATHEMATICAE
  • 1978-10. Polarizations in the classical groups in MATHEMATISCHE ZEITSCHRIFT
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    http://scigraph.springernature.com/pub.10.1007/bf02565876

    DOI

    http://dx.doi.org/10.1007/bf02565876

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