Science in China Series A: Mathematics

, Volume 44, Issue 11, pp 1413–1419 | Cite as

Geometric orbit datum and orbit covers

  • Ke Liang
  • Zixin Hou


Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.


Lie group orbit data Dixmier correspondence 


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  1. 1.
    Vogan, D., Dixmier algebras, sheets and representation theory (in Actes du colloque en I’ honneur de Jacques Dixmier), Progress in Math. 92, Boston: Birkhäiuser Verlag, 1990, 333–397.Google Scholar
  2. 2.
    McGovern, W., Dixmier Algebras and Orbit Method, Operator Algebras, Unitary Representations and Invariant Theory, Boston: Birkhäuser, 1990, 397–416.Google Scholar
  3. 3.
    Liang, K., Parabolic inductions of nilpotent geometric orbit datum, Chinese Science Bulletin (in Chinese), 1996, 41(23): 2116–2118.Google Scholar
  4. 4.
    Vogan, D., Representations of Real Reductive Lie Groups, Boston-Basel-Stuttgart: Birkh—user, 1981.MATHGoogle Scholar
  5. 5.
    Lustig, G., Spaltenstein, N., Induced unipotent class, J. London Math. Soc., 1997, 19. 41–52.CrossRefGoogle Scholar
  6. 6.
    Collingwood, D. H., McGovern, W. M., Nilpotent Orbits in Semisimple Lie Algebras, New York: Van Nostremt Reinhold, 1993.MATHGoogle Scholar

Copyright information

© Science in China Press 2001

Authors and Affiliations

  • Ke Liang
    • 1
  • Zixin Hou
    • 1
  1. 1.Department of MathematicsNankai UniversityTianjinChina

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