A tuple of commuting operators $(S_1,\dots,S_{n-1},P)$ for which the closedsymmetrized polydisc $\Gamma_n$ is a spectral set is called a$\Gamma_n$-contraction. We show that every $\Gamma_n$-contraction admits adecomposition into a $\Gamma_n$-unitary and a completely non-unitary$\Gamma_n$-contraction. This decomposition is an analogue to the canonicaldecomposition of a contraction into a unitary and a completely non-unitarycontraction. We also find new characterizations for the set $\Gamma_n$ and$\Gamma_n$-contractions.
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