  Consider an infinite homogeneous tree $T_n$ of valence $n+1$, its group
$Aut(T_n)$ of automorphisms, and the group $Hie(T_n)$ of its spheromorphisms
(hierarchomorphisms), i.~e., the group of homeomorphisms of the boundary of
$T_n$ that locally coincide with transformations defined by automorphisms. We
show that the subgroup $Aut(T_n)$ is spherical in $Hie(T_n)$, i.~e., any
irreducible unitary representation of $Hie(T_n)$ contains at most one
$Aut(T_n)$-fixed vector. We present a combinatorial description of the space of
double cosets of $Hie(T_n)$ with respect to $Aut(T_n)$ and construct a 'new'
family of spherical representations of $Hie(T_n)$. We also show that the
Thompson group has $PSL(2,\mathbb{Z})$-spherical unitary
