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Science in China Series A: Mathematics

, Volume 45, Issue 2, pp 155–164 | Cite as

On sheets of orbit covers for classical semisimple lie groups

  • Ke LiangEmail author
  • Zixin Hou
  • Linyuan Lu
Article
  • 18 Downloads

Abstract

David Vogan gave programmatic conjectures about the Dixmier’s map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed[1]. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan’s first conjecture for geometric orbit datum: the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan’s conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.

Keywords

Lie group representation of Lie group Dixmier’s map geometric orbit data 

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References

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    Vogan, D., Dixmier algebras, sheets, and representation theory, in Actes de colloque en l’honneur de Jacques Dixmier, Progress in Math. 92, Boston: Birkhäuser, 1990, 333–397.Google Scholar
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    Liang, K., Hou, Z., Geometric orbit datum and orbit covers, Science in China, Ser. A, 2001, 44(11): 1413–1419.zbMATHCrossRefMathSciNetGoogle Scholar
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    Collingwood, D. H., McGovern, W. M., Nilpotent Orbits in Semisimple Lie Algebras, New York: Van Nostrand Reinhold, 1993.zbMATHGoogle Scholar
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    Lustig, G., Intersection cohomology complexes on a reductive group, Inv. Math., 1984, 75: 205–272.CrossRefGoogle Scholar
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    Liang, K., Lu, L., The sheets and rigid orbit covers of exception Lie groups, Chinese Science Bulletin, 1998, 43(20): 1702–1707.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science in China Press 2002

Authors and Affiliations

  1. 1.Department of MathematicsNankai UniversityTianjinChina
  2. 2.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

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