Spectra of Compact Quotients of the Oscillator Group
This paper is a contribution to harmonic analysis of compact solvmanifolds. We consider the four-dimensional oscillator group Osc₁, which is a semi-direct product of the three-dimensional Heisenberg group and the real line. We classify the lattices of Osc₁ up to inner automorphisms of Osc₁. For ever...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211298 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Spectra of Compact Quotients of the Oscillator Group. Mathias Fischer and Ines Kath. SIGMA 17 (2021), 051, 48 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | This paper is a contribution to harmonic analysis of compact solvmanifolds. We consider the four-dimensional oscillator group Osc₁, which is a semi-direct product of the three-dimensional Heisenberg group and the real line. We classify the lattices of Osc₁ up to inner automorphisms of Osc₁. For every lattice in Osc₁, we compute the decomposition of the right regular representation of Osc₁ on ²(∖Osc₁) into irreducible unitary representations. This decomposition allows the explicit computation of the spectrum of the wave operator on the compact locally-symmetric Lorentzian manifold ∖Osc₁.
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| ISSN: | 1815-0659 |