On the structure of quantum permutation groups

The quantum permutation group of the set X-n = {1,..., n} corresponds to the Hopf algebra A(aut)(X-n). This is an algebra constructed with generators and relations, known to be isomorphic to C(S-n) for n <= 3, and to be infinite dimensional for n >= 4. In this paper we find an explicit representation of the algebra A(aut)(X-n), related to Clifford algebras. For n = 4 the representation is faithful in the discrete quantum group sense.