Geodesic
The Laplace operator spectrum on connected compact simple rank one and two Lie groups
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 219-234

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In the paper we suggest an algorithm for calculation of the Laplace operator spectrum for real-valued and complex-valued functions defined on a connected compact simple Lie group with a bi-invariant Riemannian metric. By means of the algorithm an explicit calculation of the spectrum is given for all connected compact simple Lie groups of rank one and two.
Keywords: Laplace operator, spectrum, Lie group representation, highest weight, Killing form. 
V. M. Svirkin. The Laplace operator spectrum on connected compact simple rank one and two Lie groups. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 219-234. http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a20/
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