This work presents a detailed study of the anisotropic series representations of the free product group \(\mathbf Z/2\mathbf Z\star \cdots \star \mathbf Z/2\mathbf Z\). These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.

Readership

Research mathematicians.

Table of Contents

• Introduction
• The Green function
• The Spectrum and the Plancherel measure
• Representations and their realization on the boundary
• Irreducibility and inequivalence
• References