Harmonic Analysis in One-Parameter Metabelian Nilmanifolds
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Harmonic Analysis in One-Parameter Metabelian Nilmanifolds
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| Creator |
Ghorbel, A.
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| 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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| Date |
2019-02-11T15:25:19Z
2019-02-11T15:25:19Z 2011 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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