A Note on $Γ_n$-isometries

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

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