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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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146800 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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| id |
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irk-123456789-1468002019-02-12T01:24:27Z Harmonic Analysis in One-Parameter Metabelian Nilmanifolds Ghorbel, A. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146800 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Ghorbel, A. |
| spellingShingle |
Ghorbel, A. Harmonic Analysis in One-Parameter Metabelian Nilmanifolds Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ghorbel, A. |
| author_sort |
Ghorbel, A. |
| title |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds |
| title_short |
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_sort |
harmonic analysis in one-parameter metabelian nilmanifolds |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146800 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ghorbela harmonicanalysisinoneparametermetabeliannilmanifolds |
| first_indexed |
2023-05-20T17:25:50Z |
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2023-05-20T17:25:50Z |
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1796153275569930240 |