Spherical functions : the spheres vs the projective spaces

In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere Sn ≃ SO(n + 1)/SO(n) and the spherical functions of the n-dimensional real projective space P n(R) ≃ SO(n + 1)/O(n). In fact, for n odd a function on SO(n + 1) is an irreducible spherical...

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Autores principales: Tirao, Juan Alfredo, Zurrián, Ignacio Nahuel
Formato: article
Lenguaje:Inglés
Publicado: 2022
Materias:
Spherical functions
Orthogonal group
Special orthogonal group
Group representations
Acceso en línea:http://hdl.handle.net/11086/27296
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-27296
record_format dspace
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Spherical functions
Orthogonal group
Special orthogonal group
Group representations
spellingShingle Spherical functions
Orthogonal group
Special orthogonal group
Group representations
Tirao, Juan Alfredo
Zurrián, Ignacio Nahuel
Spherical functions : the spheres vs the projective spaces
topic_facet Spherical functions
Orthogonal group
Special orthogonal group
Group representations
description In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere Sn ≃ SO(n + 1)/SO(n) and the spherical functions of the n-dimensional real projective space P n(R) ≃ SO(n + 1)/O(n). In fact, for n odd a function on SO(n + 1) is an irreducible spherical function of some type π ∈ ˆSO(n) if and only if it is an irreducible spherical function of some type γ ∈ ˆO(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), O(n)). Summarizing, to find all spherical functions of one pair is equivalent to do so for the other pair.
format article
author Tirao, Juan Alfredo
Zurrián, Ignacio Nahuel
author_facet Tirao, Juan Alfredo
Zurrián, Ignacio Nahuel
author_sort Tirao, Juan Alfredo
title Spherical functions : the spheres vs the projective spaces
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
publishDate 2022
url http://hdl.handle.net/11086/27296
work_keys_str_mv AT tiraojuanalfredo sphericalfunctionsthespheresvstheprojectivespaces
AT zurrianignacionahuel sphericalfunctionsthespheresvstheprojectivespaces
bdutipo_str Repositorios
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