IJPAM: Volume 29, No. 4 (2006)

EVEN AUTOMORPHISMS OF TREES AND
INDUCTIVE ALGEBRAS

Giovanni Stegel
Struttura Dipartimentale di Matematica e Fisica
Università di Sassari
2, Via Vienna, Sassari, 07100, ITALY
e-mail: stegel@uniss.it


Abstract.Let $(\pi, \, \HS)$ be a unitary representation of a locally compact group $G$. A commutative subalgebra $\A$ of $\BH$ is called $\pi$- inductive when $\pi(g)\A\pi(g^{-1})=\A$ for all $g$. The classification of maximal inductive algebras sheds light on the possible realizations of $\pi$ on function spaces. In this paper we deal with the automorphism group of a locally finite homogeneous tree and its principal series spherical representations. We show that for some exceptional representations there exists just one inductive algebra besides those known. Finally, we generalize the main results to the subgroup of even automorphisms of the tree.

Received: June 6, 2006

AMS Subject Classification: 43A99,22D10, 05C05, 47L10

Key Words and Phrases: homogeneous trees, unitary representations, operator algebras

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 29
Issue: 4