Unitary coboundary weak quasi-Hopf algebras in the Kazhdan-Lusztig-Finkelberg theorem

We construct, for every complex simple Lie algebra g and every positive integer level k, a unitary modular tensor category structure on the module category of the affine vertex operator algebra V_{g_k}, equivalent to the quantum group fusion category C(g,q,l), within the Doplicher-Roberts quantum gr