On charged fields with group symmetry and degeneracies of Verlinde's matrix S*
We present a new proof of Janson’s strong hypercontractivity inequality for the Ornstein-Uhlenbeck semigroup in holomorphic algebras associated with CAR (canonical anticommutation relations) algebras. In the one generator case we calculate optimal bounds for t such that is a contraction as a map for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.