The Vanishing of Scalar Curvature on 6 Manifolds, Einstein’s Equation, and Representation Theory

  • Bertram Kostant
Part of the Progress in Mathematics book series (PM, volume 105)

Abstract

Let G be a real semisimple Lie Group, which we may assume to be connected or even simply connected, and let g0 = Lie(G). The dual vector space of g0 will be denoted by g0*. Also, g and g* will denote the complexifications of g0 and g0*, respectively. We recall that the group G and the Lie algebra g operate on g by the adjoint representation and on g* by the so-called coadjoint representation. Moreover, set G = Ad(g). Since the bilinear form (x, y) = tr(ad x ady) on g × g is nonsingular, we can identify g and g*, which we shall do whenever it is convenient.

Keywords

Manifold Radon 

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References

  1. [K]
    Kostant, B., “The Principle of Triality and A Distinguished Unitary Representation of SO(4, 4),” Differential Geometrical Methods in Theoretical Physics, edited by K. Bleuler and M. Werner, Kluwer Academic Publishers, 1988, 65–108Google Scholar
  2. [K1]
    Kostant, B., “The Vanishing of Scalar Curvature and the Minimal Representation of SO(4, 4),” Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Birkhäuser Boston: Prog. Math. 92 1990, 85–124MathSciNetGoogle Scholar
  3. [B]
    Borho, W., A Survey on Eveloping Algebras of Semisimple Lie Algebras, I, CMS Conference Proceedings, 5 1986, 19–50MathSciNetGoogle Scholar
  4. [C]
    Chevalley, C., The Algebraic Theory of Spinors, Columbia University Press, 1954MATHGoogle Scholar
  5. [HE]
    Hawking, S. and Ellis, G., The large scale structure of space-time, Cambridge University Press, 1973CrossRefGoogle Scholar
  6. [V]
    Vogan, D., Gelfand-Kirillov dimension for Harish-Chandra modules, Inventions Math, 48 (1978), 75–98MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1992

Authors and Affiliations

  • Bertram Kostant
    • 1
  1. 1.Department of MathematicsMITCambridgeUSA

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