Generalized parity transformations in lattice Chern-Simons theory

Regularization modifies the (odd) behaviour of the Abelian Chern-Simons action under parity. This effect happens for any sensible regularization; in particular, on the lattice. However, as in the chiral symmetry case, there exist generalized parity transformations such that the regularized theory is odd, and the corresponding operator verifies a Ginsparg-Wilson like relation. We present a derivation of such a relation and of the corresponding symmetry transformations.