Polyakov loop in different representations of SU(3) at finite temperature

We investigate the Polyakov loop in different representations of SU(3) in pure gauge at finite $T$. We discuss Casimir scaling for the Polyakov loop in the deconfined phase and test and generalize the renormalization procedure for the Polyakov loop from \cite{Kaczmarek:2002mc} to arbitrary representations. In the confined phase we extract the renormalized adjoint Polyakov loop, which is finite in the thermodynamic limit. For our numerical calculations we used the tree-level improved Symanzik action on $32^3\times 4,6,8$ lattices.