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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | 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 |
| Zitieren: | 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| _version_ | 1862556216499109888 |
|---|---|
| author | Fischer, Mathias Kath, Ines |
| author_facet | Fischer, Mathias Kath, Ines |
| citation_txt | Spectra of Compact Quotients of the Oscillator Group. Mathias Fischer and Ines Kath. SIGMA 17 (2021), 051, 48 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-13T06:49:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211298 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T06:49:38Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fischer, Mathias Kath, Ines 2025-12-29T11:05:14Z 2021 Spectra of Compact Quotients of the Oscillator Group. Mathias Fischer and Ines Kath. SIGMA 17 (2021), 051, 48 pages 1815-0659 2020 Mathematics Subject Classification: 22E40; 22E27; 53C50 arXiv:1912.00050 https://nasplib.isofts.kiev.ua/handle/123456789/211298 https://doi.org/10.3842/SIGMA.2021.051 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spectra of Compact Quotients of the Oscillator Group Article published earlier |
| spellingShingle | Spectra of Compact Quotients of the Oscillator Group Fischer, Mathias Kath, Ines |
| title | Spectra of Compact Quotients of the Oscillator Group |
| title_full | Spectra of Compact Quotients of the Oscillator Group |
| title_fullStr | Spectra of Compact Quotients of the Oscillator Group |
| title_full_unstemmed | Spectra of Compact Quotients of the Oscillator Group |
| title_short | Spectra of Compact Quotients of the Oscillator Group |
| title_sort | spectra of compact quotients of the oscillator group |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211298 |
| work_keys_str_mv | AT fischermathias spectraofcompactquotientsoftheoscillatorgroup AT kathines spectraofcompactquotientsoftheoscillatorgroup |