In the representation theory of finite groups the antisymmetrizer is a well-known object, because the set of parities { ( − − 1 ) π π } forms a one-dimensional (and hence irreducible) representation of the permutation group known as the antisymmetric representation. The representation being one-dimensional, the set of parities form the character of the antisymmetric representation. The antisymmetrizer is in fact a character projection operator and is quasi-idempotent,