A product formula for spherical representations of a group of automorphisms of a homogeneous tree, I期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Donald I Cartwright Gabriella Kuhn Paolo M Soardi

Institution:	School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia ; Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Viale Sarca 202, Edificio U7, 20126 Milano, Italy ; Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Viale Sarca 202, Edificio U7, 20126 Milano, Italy

Abstract:	Let $G=\mathrm{Aut}(T)$ be the group of automorphisms of a homogeneous tree , and let $\Gamma$ be a lattice subgroup of . Let $\pi$ be the tensor product of two spherical irreducible unitary representations of . 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.

Keywords:	Spherical representation homogeneous tree

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