In several examples it has been observed that a module category of a vertex operator algebra (VOA) is equivalent to a category of representations of some quantum group. In this talk, we discuss such a duality in the case of the Virasoro VOA at generic central charge. We do not address the category of all modules of the generic Virasoro VOA, but we consider the infinitely many modules from the first row of the Kac table. Building on an explicit quantum group method of Coulomb gas integrals, we give a new proof of the fusion rules and the analyticity of compositions of intertwining operators. Crucially, we prove the associativity of the intertwining operators among the first-row modules, and find that the associativity is governed by the 6j-symbols of the quantum group Uq(sl2). This talk is based on a joint work with Kalle Kytölä.
This will be a zoom seminar:
Zoom URL: https://us02web.zoom.us/j/81055027078
Passcode: The order of the Weyl group of type $E_6$