Gauge symmetries of pure Chern-Simons theories with p-form gauge fields

The gauge symmetries of pure Chem-Simons theories with p-form gauge fields are analysed. It is shown that the number of independent gauge symmetries depends crucially on the parity of p. The case where p is odd appears to be a direct generalization of the p = 1 case and presents the remarkable feature that the timelike diffeomorphisms can be expressed in terms of the spatial diffeomorphisms and the internal gauge symmetries. In contrast, the timelike diffeomorphisms may bt:independent gauge symmetries when p is even. This happens when the number of fields and the spacetime dimension fulfil an algebraic condition which is written explicitly.