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Generalized Kostant convexity theorems
Author:
Philip Foth
Journal:
Proc. Amer. Math. Soc. 137 (2009), 297-301
MSC (2000):
Primary 53D20; Secondary 53D17, 22E15
Posted:
May 15, 2008
MathSciNet review:
2439453
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Abstract: We give a simple proof of the equality of the spectra for projections to Levi factors in the linear and non-linear cases, generalizing a classical theorem of Kostant.
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- A. Alekseev. On Poisson actions of compact Lie groups on symplectic manifolds. J. Diff. Geom., 45: 241-256, 1997. MR 1449971 (99b:58086)
- 2.
- S. Evens and J.-H. Lu. Thompson's conjecture for real semisimple Lie groups. The breadth of symplectic and Poisson geometry. Progr. Math., 232: 121-137, Birkhäuser Boston, 2005. MR 2103005 (2006c:22013)
- 3.
- P. Foth and J.-H. Lu. A Poisson structure on compact symmetric spaces. Comm. Math. Phys., 251: 557-566, 2004. MR 2102330 (2005g:53156)
- 4.
- T. Haines, M. Kapovich and J. Millson. Ideal quadrilaterals in Euclidean buildings, constant term maps for spherical Hecke rings and branching to Levi subgroups. Preprint, 2005.
- 5.
- F. Kirwan. Convexity properties of the moment mapping. III. Invent. Math., 77: 547-552, 1984. MR 759257 (86b:58042b)
- 6.
- B. Kostant. On convexity, the Weyl group and the Iwasawa decomposition. Ann. Sci. École Norm. Sup., 6: 413-455, 1973. MR 0364552 (51:806)
- 7.
- J.-H. Lu. Momentum mappings and reduction of Poisson actions. Symplectic geometry, groupoids, and integrable systems: 209-226, MSRI Publications 20, Springer, New York, 1991. MR 1104930 (92j:58036)
- 8.
- L. O'Shea and R. Sjamaar. Moment maps and Riemannian symmetric pairs. Math. Ann., 317: 415-457, 2000. MR 1776111 (2001g:53146)
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Additional Information
Philip Foth
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721-0089
Email:
foth@math.arizona.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09482-3
PII:
S 0002-9939(08)09482-3
Keywords:
Reductive Lie group,
parabolic subgroup,
Poisson Lie group,
moment map,
convexity.
Received by editor(s):
September 4, 2007
Received by editor(s) in revised form:
January 7, 2008
Posted:
May 15, 2008
Communicated by:
Gail R. Letzter
Article copyright:
© Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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