Article PDF
Avoid common mistakes on your manuscript.
References
Borel, A. andTits, J., Groupes réductifs, Inst. des Haut. Études Scient.,Publ. Math., No 27 (1965), pp. 659–754.
Eggleston, H.,Convexity, Cambridge University Press, 1958.
Harish-Chandra, Representations of semisimple Lie groups VI,Amer. J. Math., vol.78 (1956), pp. 564–628.
Helgason, S.,Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978.
Horn, A., Doubly stochastic matrices and the diagonal of a rotation matrix,Amer. J. Math., vol.76 (1954), pp. 620–630.
Koranyi, A. andWolf, J., Realization of hermitian symmetric spaces as generalized halfplanes,Ann. of Math., vol.81 (1965), pp. 265–288.
Konstant, B., On convexity the Weyl group and the Iwasawa decomposition,Ann. scient. Éc. Norm. Sup., 4e série, t.6 (1973), pp. 413–455.
Krein, M. G. andDaleckii, J. L.,Stability of solutions of differential equations in Banach space, Translations of Math. Monographs, vol.43, American Mathematical Society, 1974.
Moore, C., Compactifications of symmetric spaces II: the Cartan domains,Amer. J. Math., vol.86 (1964), pp. 358–378.
Olshansky, G., Invariant cones in Lie algebras Lie semigroups, and the holomorphic discrete series,Func. Anal. and Appl. vol.15, no. 4 (1981).
Paneitz, S. andSegal I., Quantization of wave equations and hermitian structures in partial differential varieties,Proc. Nat. Acad. Sci. USA, vol.77, no. 12 (December 1980), pp. 6943–6947.
Paneitz, S., Invariant convex cones and causality in semisimple Lie algebras and groups,J. Func. Anal., vol.43, no. 3 (1981) pp. 313–359.
Paneitz, S., inLecture Notes in Mathematics, vol. 905, Springer-Verlag, 1982.
Segal, I. E.,Mathematical cosmology and extragalactic astronomy, Academic Press, New York, 1976.
Vinberg, E., Invariant convex cones and orderings in Lie groupsFunc. Anal. and Appl., vol.14, no. 1 (1980), pp. 1–10.
Paneitz, S., Analysis in space-time bundles III. Higher spin bundlesJ. Func. Anal., in press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Paneitz, S.M. Determination of invariant convex cones in simple Lie algebras. Ark. Mat. 21, 217–228 (1983). https://doi.org/10.1007/BF02384311
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02384311