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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

Scalar Curvature Representation Theory Irreducible Unitary Representation Conformal Class Primitive Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Birkhäuser Boston 1992

Authors and Affiliations

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

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