Hostname: page-component-84b7d79bbc-4hvwz Total loading time: 0 Render date: 2024-07-29T00:07:37.870Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear Imbeddings of Self-Dual Homogeneous Cones

Published online by Cambridge University Press:  22 January 2016

I. Satake
I. Satake*
Affiliation:
University of California, Berkely
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a reductive algebraic Lie group acting linearly on a (finite-dimensional) real vector-space U with a maximal compact isotropy subgroup K and suppose that the quotient Ω = G/K is a self-dual homogeneous cone in U. Let (G′, K′) be another such pair corresponding to a self-dual homogeneous cone Ω′ in U′.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 46 , March 1972 , pp. 121 - 145
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Bourbaki, N. Groupes et algebres de Lie, Chap. 4, 5 et 6, Eléments de Math., Hermann, Paris, 1968.Google Scholar
[2] Koecher, M. (a) Positivitätsbereich in Rn , Amer. J. of Math. 79 (1957), 575–596. (b) Analysis in reellen Jordan Algebren, Nachr. Akad. Wiss. Gõttingen Math-Phys. Kl. Ha (1958), 67–74. (c) Die Geodätischen von Positivitâtsbereichen, Math. Ann. 135 (1958), 192–202.Google Scholar
[3] Satake, I. (a) Holomorphic imbeddings of symmetric domains into a Siegel space, Amer. J. of Math. 87 (1965), 425–461. (b) Clifford algebras and families of abelian varieties, Nagoya Math. J. 27 (1966), 435–446; Corrections, ibid. 31 (1968), 295–296. (c) Symplectic representations of algebraic groups satisfying a certain analyticity condition, Acta Math. 117 (1967), 425–461.CrossRefGoogle Scholar
[4] Vinberg, E.B. (a) Homogeneous cones, Dokl. Akad. Nauk SSSR 133 (1960), 9–12 (= Soviet Math. Dokl. 1 (1961), 787–790). (b) The theory of homogeneous convex cones, Trudy Moskov. Mat. Obsc. 12 (1963), 303–358 (=Trans. of Moscow Math. Soc. 1963, 340–403).Google Scholar