Geodesic
On the Unitarized Adjoint Representation of a Semisimple Lie Group II
Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1217-1222

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Let G be a connected semisimple Lie group with Lie algebra . Lebesgue measure on is invariant under the adjoint action of G; and so there is a natural unitary representation TG of G on L2 given by 
Lipsman, Ronald L. On the Unitarized Adjoint Representation of a Semisimple Lie Group II. Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1217-1222. doi: 10.4153/CJM-1977-121-7
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[1] 1. Helgason, S., Differential geometry and symmetric spaces (Academic Press, New York, 1962). Google Scholar

[2] 2. Lipsman, R., Group representations (Springer-Verlag Lecture Notes in Mathematics, no. 388, 1974). Google Scholar

[3] 3. Lipsman, R. On the unitary representation of a semisimple Lie group given by the invariant integral on its Lie algebra, Advances in Math., to appear. Google Scholar

[4] 4. Lipsman, R. On the unitarized adjoint representation of a semisimple Lie group III, to appear. Google Scholar

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