Generalized Kostant convexity theorems
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- by Philip Foth
- Proc. Amer. Math. Soc. 137 (2009), 297-301
- DOI: https://doi.org/10.1090/S0002-9939-08-09482-3
- Published electronically: May 15, 2008
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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.References
- A. Yu. Alekseev, On Poisson actions of compact Lie groups on symplectic manifolds, J. Differential Geom. 45 (1997), no. 2, 241–256. MR 1449971
- Sam Evens and Jiang-Hua Lu, Thompson’s conjecture for real semisimple Lie groups, The breadth of symplectic and Poisson geometry, Progr. Math., vol. 232, Birkhäuser Boston, Boston, MA, 2005, pp. 121–137. MR 2103005, DOI 10.1007/0-8176-4419-9_{5}
- P. Foth and J.-H. Lu, A Poisson structure on compact symmetric spaces, Comm. Math. Phys. 251 (2004), no. 3, 557–566. MR 2102330, DOI 10.1007/s00220-004-1178-4
- 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.
- V. Guillemin and S. Sternberg, Convexity properties of the moment mapping. II, Invent. Math. 77 (1984), no. 3, 533–546. MR 759258, DOI 10.1007/BF01388837
- Bertram Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413–455 (1974). MR 364552
- Jiang-Hua Lu, Momentum mappings and reduction of Poisson actions, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 209–226. MR 1104930, DOI 10.1007/978-1-4613-9719-9_{1}5
- Luis O’Shea and Reyer Sjamaar, Moment maps and Riemannian symmetric pairs, Math. Ann. 317 (2000), no. 3, 415–457. MR 1776111, DOI 10.1007/PL00004408
Bibliographic Information
- Philip Foth
- Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721-0089
- Email: foth@math.arizona.edu
- Received by editor(s): September 4, 2007
- Received by editor(s) in revised form: January 7, 2008
- Published electronically: May 15, 2008
- Communicated by: Gail R. Letzter
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 297-301
- MSC (2000): Primary 53D20; Secondary 53D17, 22E15
- DOI: https://doi.org/10.1090/S0002-9939-08-09482-3
- MathSciNet review: 2439453