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

Cartwright, Donald; Kuhn, Gabriella; Soardi, Paolo

doi:10.1090/S0002-9947-00-02584-8

A product formula for spherical representations of a group of automorphisms of a homogeneous tree, I
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by Donald I. Cartwright, Gabriella Kuhn and Paolo M. Soardi PDF

Trans. Amer. Math. Soc. 353 (2001), 349-364 Request permission

Abstract:

Let $G=\mathrm {Aut}(T)$ be the group of automorphisms of a homogeneous tree $T$, and let $\Gamma$ be a lattice subgroup of $G$. Let $\pi$ be the tensor product of two spherical irreducible unitary representations of $G$. We give an explicit decomposition of the restriction of $\pi$ to $\Gamma$. We also describe the spherical component of $\pi$ explicitly, and this decomposition is interpreted as a multiplication formula for associated orthogonal polynomials.

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