  We explicitly compute a monoidal subcategory of the monoidal center of
Deligne's interpolation category Rep(S_t), for t not necessarily a natural
number, and we show that this subcategory is a ribbon category. For t=n, a
natural number, there exists a functor onto the braided monoidal category of
modules over the Drinfeld double of S_n which is essentially surjective and
full. Hence the new ribbon category interpolates the categories of crossed
modules over the symmetric groups. As an application, we obtain invariants of
framed ribbon links which are polynomials in the interpolating variable t.
These polynomials interpolate untwisted Dijkgraaf-Witten invariants of the
symmetric groups.
