  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.

High Energy Physics - Lattice