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Liczba wyników
1996 | 71 | 1 | 107-110

Tytuł artykułu

On the Moment Map of a Multiplicity Free Action

Treść / Zawartość

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].

Rocznik

Tom

71

Numer

1

Strony

107-110

Daty

wydano
1996
otrzymano
1995-10-30

Twórcy

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

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