Harmonic Analysis in One-Parameter Metabelian Nilmanifolds
Let G be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that G contains a discrete cocompact subgroup. Given a discrete cocompact subgroup Γ of G, we define the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146800 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds / A. Ghorbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862738698902175744 |
|---|---|
| author | Ghorbel, A. |
| author_facet | Ghorbel, A. |
| citation_txt | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds / A. Ghorbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let G be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that G contains a discrete cocompact subgroup. Given a discrete cocompact subgroup Γ of G, we define the quasi-regular representation τ=indΓG1 of G. The basic problem considered in this paper concerns the decomposition of τ into irreducibles. We give an orbital description of the spectrum, the multiplicity function and we construct an explicit intertwining operator between τ and its desintegration without considering multiplicities. Finally, unlike the Moore inductive algorithm for multiplicities on nilmanifolds, we carry out here a direct computation to get the multiplicity formula.
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| first_indexed | 2025-12-07T20:05:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146800 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:05:16Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ghorbel, A. 2019-02-11T15:25:19Z 2019-02-11T15:25:19Z 2011 Harmonic Analysis in One-Parameter Metabelian Nilmanifolds / A. Ghorbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. 1815-0659 https://nasplib.isofts.kiev.ua/handle/123456789/146800 Let G be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that G contains a discrete cocompact subgroup. Given a discrete cocompact subgroup Γ of G, we define the quasi-regular representation τ=indΓG1 of G. The basic problem considered in this paper concerns the decomposition of τ into irreducibles. We give an orbital description of the spectrum, the multiplicity function and we construct an explicit intertwining operator between τ and its desintegration without considering multiplicities. Finally, unlike the Moore inductive algorithm for multiplicities on nilmanifolds, we carry out here a direct computation to get the multiplicity formula. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Harmonic Analysis in One-Parameter Metabelian Nilmanifolds Article published earlier |
| spellingShingle | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds Ghorbel, A. |
| title | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_full | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_fullStr | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_full_unstemmed | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_short | Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_sort | harmonic analysis in one-parameter metabelian nilmanifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146800 |
| work_keys_str_mv | AT ghorbela harmonicanalysisinoneparametermetabeliannilmanifolds |