On the Moment Map of a Multiplicity Free Action
Andrzej Daszkiewicz; Tomasz Przebinda
Colloquium Mathematicae (1996)
- Volume: 71, Issue: 1, page 107-110
- ISSN: 0010-1354
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topDaszkiewicz, Andrzej, and Przebinda, Tomasz. "On the Moment Map of a Multiplicity Free Action." Colloquium Mathematicae 71.1 (1996): 107-110. <http://eudml.org/doc/210415>.
@article{Daszkiewicz1996,
abstract = {The purpose of this note is to show that the Orbit Conjecture of C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff [BJLR1] is true. Another proof of that fact has been given by those authors in [BJLR2]. Their proof is based on their earlier results, announced together with the conjecture in [BJLR1]. We follow another path: using a geometric quantization result of Guillemin-Sternberg [G-S] we reduce the conjecture to a similar statement for a projective space, which is a special case of a characterization of projective smooth spherical varieties due to Brion [B2].},
author = {Daszkiewicz, Andrzej, Przebinda, Tomasz},
journal = {Colloquium Mathematicae},
keywords = {spherical variety; connected reductive complex group; positive definite hermitian form; moment map; Lie algebra; orbit conjecture},
language = {eng},
number = {1},
pages = {107-110},
title = {On the Moment Map of a Multiplicity Free Action},
url = {http://eudml.org/doc/210415},
volume = {71},
year = {1996},
}
TY - JOUR
AU - Daszkiewicz, Andrzej
AU - Przebinda, Tomasz
TI - On the Moment Map of a Multiplicity Free Action
JO - Colloquium Mathematicae
PY - 1996
VL - 71
IS - 1
SP - 107
EP - 110
AB - The purpose of this note is to show that the Orbit Conjecture of C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff [BJLR1] is true. Another proof of that fact has been given by those authors in [BJLR2]. Their proof is based on their earlier results, announced together with the conjecture in [BJLR1]. We follow another path: using a geometric quantization result of Guillemin-Sternberg [G-S] we reduce the conjecture to a similar statement for a projective space, which is a special case of a characterization of projective smooth spherical varieties due to Brion [B2].
LA - eng
KW - spherical variety; connected reductive complex group; positive definite hermitian form; moment map; Lie algebra; orbit conjecture
UR - http://eudml.org/doc/210415
ER -
References
top- [BJLR1] C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff, The moment map for a multiplicity-free action, Bull. Amer. Math. Soc. 31 (1994), 185-190. Zbl0829.22014
- [BJLR2] C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff, A geometric criterion for Gelfand pairs associated with the Heisenberg group, Pacific J. Math., to appear. Zbl0868.22015
- [B1] M. Brion, Spherical Varieties: An Introduction, in: Topological Methods in Algebraic Transformation Groups, H. Kraft, T. Petrie and G. Schwarz (eds.), Progr. Math. 80, Birkhäuser, Boston, 1989, 11-26.
- [B2] M. Brion, Sur l'image de l'application moment, in: Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin, M.-P. Mallavin (ed.), Lecture Notes in Math. 1296, Springer, Berlin, 1987, 177-192.
- [G-S] V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), 515-538. Zbl0503.58018
- [O-V] A. L. Onishchik and E. B. Vinberg (eds.), Lie Groups and Lie Algebras III, Springer, Berlin, 1994.
- [Se] F. J. Servedio, Prehomogeneous vector spaces and varieties, Trans. Amer. Math. Soc. 176 (1973), 421-444. Zbl0266.20043
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