  We study a $q$-deformation for the semi-direct product of the symmetric group
$S_n$ with the Clifford algebra on $n$ anticommuting generators. We obtain a
$q$-version of the projective analogue for the classical Young symmetrizer
found by the second author [Adv. Math. 127(1997), 190-257]. Our main tool is an
analogue of the Hecke algebra of complex valued functions on the group $GL_{n}$
over a $p$-adic field relative to the Iwahori subgroup.
