  It is a well known fact from the group theory that irreducible tensor
representations of classical groups are suitably characterized by irreducible
representations of the symmetric groups. However, due to their different
nature, vector and spinor representations are only connected and not united in
such description.
  Clifford algebras are an ideal tool with which to describe symmetries of
multi-particle systems since they contain spinor and vector representations
within the same formalism, and, moreover, allow for a complete study of all
classical Lie groups. In this work, together with an accompanying work also
presented at this conference, an analysis of q-symmetry -- for generic q's --
based on the ordinary symmetric groups is given for the first time. We
construct q-Young operators as Clifford idempotents and the Hecke algebra
representations in ideals generated by these operators. Various relations as
orthogonality of representations and completeness are given explicitly, and the
symmetry types of representations is discussed. Appropriate q-Young diagrams
and tableaux are given. The ordinary case of the symmetric group is obtained in
the limit q \to 1. All in all, a toolkit for Clifford algebraic treatment of
multi-particle systems is provided. The distinguishing feature of this paper is
that the Young operators of conjugated Young diagrams are related by Clifford
reversion, connecting Clifford algebra and Hecke algebra features. This
contrasts the purely Hecke algebraic approach of King and Wybourne, who do not
embed Hecke algebras into Clifford algebras.
