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

Chapter

## Abstract

Let *G* be a real semisimple Lie Group, which we may assume to be connected or even simply connected, and let g_{0} = Lie(*G*). The dual vector space of g_{0} will be denoted by g_{0}*. Also, g and g* will denote the complexifications of g_{0} and g_{0}*, 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* _{ℂ} = *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
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## References

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## Copyright information

© Birkhäuser Boston 1992