Using face algebras (i.e. algebras of L-operators of IRF models), we
construct modular tensor categories with positive definite inner product, whose
fusion rules and S-matrices are the same as (or slightly different from) those
obtained by Uqβ(slNβ) at roots of unity. Also we obtain state-sums
of ABF models on framed links which give quantum SU(2)-invariants of
corresponding 3-manifolds.Comment: AMS-LaTeX, 36 pages, to appear in Commun. Math. Phy