18 research outputs found
Matrix Valued Spherical Functions Associated to the Complex Projective Plane
The main purpose of this paper is to compute all irreducible spherical
functions on G=\SU(3) of arbitrary type , where
. This is
accomplished by associating to a spherical function on a matrix
valued function on the complex projective plane . It
is well known that there is a fruitful connection between the hypergeometric
function of Euler and Gauss and the spherical functions of trivial type
associated to a rank one symmetric pair . But the relation of spherical
functions of types of dimension bigger than one with classical analysis, has
not been worked out even in the case of an example of a rank one pair. The
entries of are solutions of two systems of ordinary differential equations.
There is no ready made approach to such a pair of systems, or even to a single
system of this kind. In our case the situation is very favorable and the
solution to this pair of systems can be exhibited explicitely in terms of a
special class of generalized hypergeometric functions .Comment: 70 pages, 1 figur