On the Moment Map of a Multiplicity Free Action

• Autorzy: Andrzej Daszkiewicz , Tomasz Przebinda
• Języki publikacji: EN

Abstrakty

EN

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].

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 71
• Numer: 1
• Strony: 107-110

Daty

wydano

1996

otrzymano

1995-10-30

Twórcy

autor

Andrzej Daszkiewicz

• Department of Mathematics, Nicholas Copernicus University, 87-100 Toruń, Poland

autor

Tomasz Przebinda

• Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, U.S.A.

Bibliografia

• [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.
• [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.
• [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.
• [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.