Geodesic
The spectrum of the Laplace operator on connected compact simple Lie groups of rank four.~II
Matematičeskie trudy, Tome 22 (2019) no. 2, pp. 34-53

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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 $A_4$ and $F_4$. 
@article{MT_2019_22_2_a2,
     author = {I. A. Zubareva},
     title = {The spectrum of the {Laplace} operator on connected compact simple {Lie} groups of rank {four.~II}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {34--53},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2019_22_2_a2/}
}
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I. A. Zubareva. The spectrum of the Laplace operator on connected compact simple Lie groups of rank four.~II. Matematičeskie trudy, Tome 22 (2019) no. 2, pp. 34-53. http://geodesic.mathdoc.fr/item/MT_2019_22_2_a2/