Related Web Sites
Stembridge has some software and data related to spherical unitary
John's Research Data
and other useful stuff and his Coxeter and
Weyl packages for Maple are also relevant.
Jiu-Kang Yu has some nice pictures, some 3-dimensional:
rank 2 and 3 in the dominant chamber,
type A, and
Dan Barbasch has some preprints
on spherical unitary representations and other things.