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The spectra of the Laplace operators on connected compact simple Lie groups of rank 3


We expose explicit calculations of the spectra of the Laplace operators for smooth real or complex functions on all connected compact simple Lie groups of rank 3 with bi-invariant Riemannian metric and establish the relationship of the obtained formulas with number theory and integer-valued ternary and binary quadratic forms.

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Correspondence to V. N. Berestovskiĭ.

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Original Russian Text © V.N. Berestovski˘ı, I.A. Zubareva, and V.M. Svirkin, 2016, published in Matematicheskie Trudy, 2016, Vol. 19, No. 1, pp. 3–45.

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Berestovskiĭ, V.N., Zubareva, I.A. & Svirkin, V.M. The spectra of the Laplace operators on connected compact simple Lie groups of rank 3. Sib. Adv. Math. 26, 153–181 (2016).

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  • Laplace operator
  • spectrum
  • representation of a group
  • Killing form