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: | , |
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| Formato: | article |
| Lenguaje: | Inglés |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | http://hdl.handle.net/11086/27296 |
| Aporte de: |
| Sumario: | 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. |
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