Artículo
Spherical Functions: The Spheres Vs. The Projective Spaces
Fecha de publicación:
01/2014
Editorial:
Heldermann Verlag
Revista:
Journal Of Lie Theory
ISSN:
0949-5932
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
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Identificadores
Colecciones
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
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
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