Boundary Representations of the Free Group, I

Gabriella Kuhn and Tim Steger
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Gabriella Kuhn: Università degli Studi di Milano
Tim Steger: University of Chicago

A chapter in Harmonic Analysis and Discrete Potential Theory, 1992, pp 85-91 from Springer

Abstract: Abstract Let Г be a noncommutative free group on finitely many generators. Fix a basis for Г and let A consist of the basis elements and their inverses. The Cayley graph of Г with respect to A, denoted by τ, has Г as its vertex set, and has an edge between each pair of vertices {x, xa} for x ∈ Г and a ∈ A. The left action of Г on itself clearly preserves the graph structure. It is well known that τ is an infinite tree and is homogeneous, meaning that each vertex lies on the same number of edges.

Keywords: Unitary Representation; Cayley Graph; Boundary Representation; Regular Representation; Left Action (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-1-4899-2323-3_7

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