Geodesic
The spectrum of the Laplace operator on connected compact simple Lie groups of rank four
Matematičeskie trudy, Tome 19 (2016) no. 2, pp. 42-85

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In the present article, we explicitly compute the spectrum of the Laplace operator on smooth real-valued and complex-valued functions on connected compact simple Lie groups of rank four with a bi-invariant Riemannian metrics that correspond to the root systems $B_4$, $C_4$, and $D_4$. We also find a connection between the obtained formulas, number theory, and integral quadratic forms in two, three, and four variables. 
@article{MT_2016_19_2_a1,
     author = {I. A. Zubareva},
     title = {The spectrum of the {Laplace} operator on connected compact simple {Lie} groups of rank four},
     journal = {Matemati\v{c}eskie trudy},
     pages = {42--85},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2016_19_2_a1/}
}
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I. A. Zubareva. The spectrum of the Laplace operator on connected compact simple Lie groups of rank four. Matematičeskie trudy, Tome 19 (2016) no. 2, pp. 42-85. http://geodesic.mathdoc.fr/item/MT_2016_19_2_a1/