Spherical Functions: The Spheres Vs. The Projective Spaces
- Autores
- Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel
- Año de publicación
- 2014
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R})\simeq\SO(n+1)/\mathrm{O}(n)$. In fact, for n odd a function on $\SO(n+1)$ is an irreducible spherical function of some type $\pi\in\hat\SO(n)$ if and only if it is an irreducible spherical function of some type γ∈O^(n). When n is even this is also true for certain types, and in the other cases we exhibit a clear correspondence between the irreducible spherical functions of both pairs $(\SO(n+1),\SO(n))$ and $(\SO(n+1),\mathrm{O}(n))$. Summarizing, to find all spherical functions of one pair is equivalent to do so for the other pair.
Fil: Tirao, Juan Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Zurrián, Ignacio Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina - Materia
-
Spherical Functions
Orthogonal Group
Special Orthogonal Group
Group Representations. - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/32176
Ver los metadatos del registro completo
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Spherical Functions: The Spheres Vs. The Projective SpacesTirao, Juan AlfredoZurrián, Ignacio NahuelSpherical FunctionsOrthogonal GroupSpecial Orthogonal GroupGroup Representations.https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R})\simeq\SO(n+1)/\mathrm{O}(n)$. In fact, for n odd a function on $\SO(n+1)$ is an irreducible spherical function of some type $\pi\in\hat\SO(n)$ if and only if it is an irreducible spherical function of some type γ∈O^(n). When n is even this is also true for certain types, and in the other cases we exhibit a clear correspondence between the irreducible spherical functions of both pairs $(\SO(n+1),\SO(n))$ and $(\SO(n+1),\mathrm{O}(n))$. Summarizing, to find all spherical functions of one pair is equivalent to do so for the other pair.Fil: Tirao, Juan Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Zurrián, Ignacio Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaHeldermann Verlag2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/32176Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel; Spherical Functions: The Spheres Vs. The Projective Spaces; Heldermann Verlag; Journal Of Lie Theory; 24; 1-2014; 147-1570949-5932CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1207.0024info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:51:49Zoai:ri.conicet.gov.ar:11336/32176instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:51:49.396CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Spherical Functions: The Spheres Vs. The Projective Spaces |
| title |
Spherical Functions: The Spheres Vs. The Projective Spaces |
| spellingShingle |
Spherical Functions: The Spheres Vs. The Projective Spaces Tirao, Juan Alfredo Spherical Functions Orthogonal Group Special Orthogonal Group Group Representations. |
| title_short |
Spherical Functions: The Spheres Vs. The Projective Spaces |
| title_full |
Spherical Functions: The Spheres Vs. The Projective Spaces |
| title_fullStr |
Spherical Functions: The Spheres Vs. The Projective Spaces |
| title_full_unstemmed |
Spherical Functions: The Spheres Vs. The Projective Spaces |
| title_sort |
Spherical Functions: The Spheres Vs. The Projective Spaces |
| dc.creator.none.fl_str_mv |
Tirao, Juan Alfredo Zurrián, Ignacio Nahuel |
| author |
Tirao, Juan Alfredo |
| author_facet |
Tirao, Juan Alfredo Zurrián, Ignacio Nahuel |
| author_role |
author |
| author2 |
Zurrián, Ignacio Nahuel |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Spherical Functions Orthogonal Group Special Orthogonal Group Group Representations. |
| topic |
Spherical Functions Orthogonal Group Special Orthogonal Group Group Representations. |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R})\simeq\SO(n+1)/\mathrm{O}(n)$. In fact, for n odd a function on $\SO(n+1)$ is an irreducible spherical function of some type $\pi\in\hat\SO(n)$ if and only if it is an irreducible spherical function of some type γ∈O^(n). When n is even this is also true for certain types, and in the other cases we exhibit a clear correspondence between the irreducible spherical functions of both pairs $(\SO(n+1),\SO(n))$ and $(\SO(n+1),\mathrm{O}(n))$. Summarizing, to find all spherical functions of one pair is equivalent to do so for the other pair. Fil: Tirao, Juan Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina Fil: Zurrián, Ignacio Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina |
| description |
In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R})\simeq\SO(n+1)/\mathrm{O}(n)$. In fact, for n odd a function on $\SO(n+1)$ is an irreducible spherical function of some type $\pi\in\hat\SO(n)$ if and only if it is an irreducible spherical function of some type γ∈O^(n). When n is even this is also true for certain types, and in the other cases we exhibit a clear correspondence between the irreducible spherical functions of both pairs $(\SO(n+1),\SO(n))$ and $(\SO(n+1),\mathrm{O}(n))$. Summarizing, to find all spherical functions of one pair is equivalent to do so for the other pair. |
| publishDate |
2014 |
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2014-01 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
| status_str |
publishedVersion |
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http://hdl.handle.net/11336/32176 Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel; Spherical Functions: The Spheres Vs. The Projective Spaces; Heldermann Verlag; Journal Of Lie Theory; 24; 1-2014; 147-157 0949-5932 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/32176 |
| identifier_str_mv |
Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel; Spherical Functions: The Spheres Vs. The Projective Spaces; Heldermann Verlag; Journal Of Lie Theory; 24; 1-2014; 147-157 0949-5932 CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
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eng |
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info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1207.0024 |
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openAccess |
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Heldermann Verlag |
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