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manuscripta mathematica

, Volume 62, Issue 2, pp 205–217 | Cite as

Separated orbits for certain non-reductive subgroups

  • Frank D. Grosshans
Article
  • 32 Downloads

Abstract

In this paper, we extend central portions of the geometric invariant theory for reductive groups G to nonreductive subgroups H satisfying the codimension 2 condition on G/H. First, the separated orbits for such subgroups are described using a one-parameter subgroup criterion. Second, the desired theorems concerning quotient varieties for spaces of separated orbits are proved.

Keywords

Number Theory Algebraic Geometry Topological Group Central Portion Invariant Theory 
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References

  1. [1]
    BOURBAKI, N.: Eléments de mathématique. Vol. XXXIV, Groupes et algébres de Lie, Chapter VI. Paris: Hermann 1968Google Scholar
  2. [2]
    DIXMIER, J. and REYNAUD, M.: Sur le quotient d'une varieté algébrique par un groupe algébrique. Mathematical analysis and applications, Part A. Advances in Math. Supplementary Studies, Vol. 7A, 327–344 (1981)Google Scholar
  3. [3]
    GROSSHANS, F.: The invariants of unipotent radicals of parabolic subgroups. Invent. Math. 73, 1–9 (1983)Google Scholar
  4. [4]
    GROSSHANS, F.: Constructing invariant polynomials via Tschirnhaus transformations. In: Invariant Theory, pp. 95–102. Lect. Notes Math. 1278. Berlin-Heidelberg-New York: Springer 1987Google Scholar
  5. [5]
    KEMPF, G.R.: Instability in invariant theory. Annals of Math. 108, 299–316 (1978)Google Scholar
  6. [6]
    NEWSTEAD, P.E.: Introduction to moduli problems and orbit spaces. Bombay: Tata Institute 1978Google Scholar
  7. [7]
    RICHARDSON, R.W.: Affine coset spaces of reductive algebraic groups. Bull. London Math. Soc. 9, 38–41 (1977)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Frank D. Grosshans
    • 1
  1. 1.Department of Mathematical SciencesWest Chester UniversityWest ChesterUSA

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