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LetG =A ut(T ) be the group of automorphisms of a homogeneous tree T , and let be a lattice subgroup of G.L et be the tensor product of two spherical irreducible unitary representations of G. We give an explicit decomposition of the restriction of to . We also describe the spherical com- ponent of explicitly, and this decomposition is interpreted as a multiplication formula for associated orthogonal polynomials.

A product formula for spherical representations of a group of automorphisms of a homogeneous tree, I