A Note on ${\Gamma }_n$-isometries

Abstract

In this note we characterize the distinguished boundary of the symmetrized polydisc and thereby develop a model theory for ${\Gamma }_n$-isometries along the lines of \cite{AY}. We further prove that for invariant subspaces of ${\Gamma }_n$-isometries, similar to the case $n=2$ \cite{S}, Beurling-Lax-Halmos type representation holds.

Submitted