CIEM 05476
CENTRO DE INVESTIGACION Y ESTUDIOS DE MATEMATICA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Spherical Functions associated to three dimensional sphere.
Autor/es:
INÉS PACHARONI; JUAN A. TIRAO; IGNACIO ZURRIÁN
Lugar:
Santiago, Chile.
Reunión:
Congreso; III CLAM Congreso Latino Americano de Matemáticos; 2009
Institución organizadora:
UMALCA
Resumen:
In this paper, we determine all irreducible spherical functions of any K-type associated to the pair (G;K) = (SO(4); SO(3)). This is accomplished by associating to a vector valued function H = H(u) of a real variable u, which is analytic at u = 0 and its components are solutions of two coupled systems of ordinary di erential equations. By an appropriate conjugation in- volving Hahn polynomials we uncouple one of the systems then this is taken to a system of hypergeometric equations, leading to express the entries of H in terms of Gegenbauer´s polynomials. Finally, we identify those simultane- ous solutions and use the representation theory of SO(4) to characterize all irreducible spherical functions.
