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Representation Theory

ISSN 1088-4165

 
 

 

Orbits in the flag variety and images
of the moment map for classical groups I


Author: Atsuko Yamamoto
Journal: Represent. Theory 1 (1997), 329-404
MSC (1991): Primary 22E46
DOI: https://doi.org/10.1090/S1088-4165-97-00007-1
Published electronically: November 14, 1997
MathSciNet review: 1479152
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Abstract | References | Similar Articles | Additional Information

Abstract: We propose algorithms to get representatives and the images of the moment map of conormal bundles of $GL(p,\mbox{\bf C})\times GL(q,\mbox{\bf C})$-orbits in the flag variety of $GL(p+q,\mbox{\bf C})$, and $GL(p+q,\mbox{\bf C})$-orbits and $Sp(p,\mbox{\bf C})\times Sp(q,\mbox{\bf C})$-orbits in the flag variety of $Sp(p+q,\mbox{\bf C})$ and their signed Young diagrams.


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  • 1. W. Borho and J. Brylinski, Differential operators on homogeneous spaces. III, Invent. Math., 80 (1985), 1-68. MR 87i:22045
  • 2. D. Collingwood and W. McGovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold, New York, 1993. MR 94j:17001
  • 3. D. Garfinkle, The annihilators of irreducible Harish-Chandra modules for $SU(p,q)$ and other type $A_{n-1}$ groups, Amer. J. Math., 115 (1993), 305-369. MR 94i:22037
  • 4. B. Kostant and S. Rallis, Orbits and representations associated with symmetric spaces, Amer. J. Math., 93 (1971), 753-809. MR 47:399
  • 5. T. Matsuki, The orbits of affine symmetric spaces under the action of minimal parabolic subgroups, J. Math. Soc. Japan, 31 (1979), 331-357. MR 81a:53049
  • 6. T. Matsuki and T. Oshima, Embeddings of discrete series into principal series, The orbit Method in Representation theory, Progress in Math., 82 (1988), Birkhäuser, Boston, MA, 147-175. MR 92d:22020
  • 7. T. Oshima, Asymptotic behavior of spherical functions on semisimple symmetric spaces, Advanced Studies in Pure Math., 14 (1988), 561-610. MR 91c:22018
  • 8. W. Rossmann, The structure of semisimple symmetric spaces, Queen's papers, Pure Appl. Math., 48 (1978), 513-520. MR 58:18284
  • 9. D. Vogan, Irreducible characters of semisimple Lie groups III, Invent. Math., 71 (1983), 381-417. MR 84h:22036
  • 10. A. Yamamoto, $GL(p,{\mathbb{C}})\times GL(q,{\mathbb{C}})$-orbits on the flag variety of $GL(p+q,{\mathbb{C}})$ and the image under the moment map, (1993), Master thesis, Univ. of Tokyo, Japan, (In Japanese).
  • 11. A. Yamamoto, Orbits in the flag variety and images of the moment map for $U(p,q)$, Proc. Japan Acad., 72. Ser. A, (1996), 114-117. MR 97g:22011

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Additional Information

Atsuko Yamamoto
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, Komaba Tokyo 153, Japan
Email: atsuko@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S1088-4165-97-00007-1
Received by editor(s): August 21, 1996
Received by editor(s) in revised form: May 22, 1997
Published electronically: November 14, 1997
Additional Notes: The author was supported by the Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists.
Article copyright: © Copyright 1997 American Mathematical Society

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