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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211298 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Spectra of Compact Quotients of the Oscillator Group. Mathias Fischer and Ines Kath. SIGMA 17 (2021), 051, 48 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 𝐿 in Osc₁, we compute the decomposition of the right regular representation of Osc₁ on 𝐿²(𝐿∖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 𝐿∖Osc₁.
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| ISSN: | 1815-0659 |