Spherical functions on the space of p-adic unitary hermitian matrices

Let $X$ be the space of unitary unramified hermitian matrices of size $2n$ over a $p$-adic field, and
consider spherical functions on $X$, i.e. common eigenfunctions on $X$ with respect to the action of the Hecke algebra. A typical one
$w(x; z)$, $x$ in $X$, $z$ in $C^n$, is given by Poisson transform from relative invariants on X. The main term of
$w(x; z)$ is given by a specialization of Macdonald polynomial, and one can parametrize all spherical functions by using $w(x;z)$, which is
$2^n$-dimensional for each $z$ in $C^n$.