Vol. 72, No. 2, 1977

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Affine open orbits, reductive isotropy groups, and dominant gradient morphisms; a theorem of Mikio Sato

Frank Servedio

Vol. 72 (1977), No. 2, 537–545
Abstract

An algebraic proof is given for a theorem of M. Sato. The theorem gives criteria for the open orbit in a prehomogeneous vector space under a reductive group to be an affine variety. The following conditions are equivalent:

  1. O(G) the open orbit is an affine variety.
  2. GX the isotropy subgroup of X in O(G) is reductive.
  3. There exists a semi-invariant form P of degree r 2 such that grad P : V V is a dominant morphism of affine varieties.

Mathematical Subject Classification 2000
Primary: 14L15
Secondary: 20G20
Milestones
Received: 4 November 1976
Revised: 23 March 1977
Published: 1 October 1977
Authors
Frank Servedio