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Strongly isotropy irreducible spaces whose Laplacians have all their eigenspaces irreducible

  • Emilio A. Lauret
  • Fiorela Rossi Bertone
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Abstract

Let H be a closed subgroup of a compact connected Lie group G such that G/H is simply connected, the action of G on G/H is almost effective, and G/H is a strongly isotropy irreducible space. The smallest positive eigenvalue of the Laplace-Beltrami operator Δ associated to the standard metric on G/H was recently computed. In this article we obtain a second non-zero eigenvalue of Δ. As a consequence, we prove that all eigenspaces of the Laplacian are irreducible as G-modules if and only if (G,H) is a compact symmetric pair of real rank one, or (G,H) is equal to (G2,SU(3)) or (Spin(7),G2).

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Cite

BibTeXRIS
BibTeX
@misc{lauret2026strongly,
  title = {{Strongly isotropy irreducible spaces whose Laplacians have all their eigenspaces irreducible}},
  author = {Emilio A. Lauret and Fiorela Rossi Bertone},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15113},
  eprint = {2610.15113},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15113},
}
RIS
TY  - UNPB
TI  - Strongly isotropy irreducible spaces whose Laplacians have all their eigenspaces irreducible
AU  - Emilio A. Lauret
AU  - Fiorela Rossi Bertone
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.15113
UR  - https://arxiv.org/abs/2610.15113
AB  - Let H be a closed subgroup of a compact connected Lie group G such that G/H is simply connected, the action of G on G/H is almost effective, and G/H is a strongly isotropy irreducible space. The smallest positive eigenvalue of the Laplace-Beltrami operator Δ associated to the standard metric on G/H was recently computed. In this article we obtain a second non-zero eigenvalue of Δ. As a consequence, we prove that all eigenspaces of the Laplacian are irreducible as G-modules if and only if (G,H) is a compact symmetric pair of real rank one, or (G,H) is equal to (G_2,SU(3)) or (Spin(7),G_2).
ER  -