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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. Weshow that the subgroup $Aut(T_n)$ is spherical in $Hie(T_n)$, i.~e., anyirreducible unitary representation of $Hie(T_n)$ contains at most one$Aut(T_n)$-fixed vector. We present a combinatorial description of the space ofdouble 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 theThompson group has $PSL(2,\mathbb{Z})$-spherical unitary

On spherical unitary representations of groups of spheromorphisms of Bruhat--Tits trees