Wenjun Niu (UC Davis) “Quantum-supergroup-extensions of U_q^H(sl(2)) at the fourth root of unity”

Seminar Organizer

Event Details

Abstract: In work to appear with Ballin-Creutzig-Dimofte, we constructed vertex operator algebras associated to A and B twists of 3d N=4 abelian gauge theories. These are boundary VOAs supported on holomorphic boundary conditions of Costello-Gaiotto. For the B twist, the vertex algebra V_B is a simple current extension of an affine Lie superalgebra, and using the work of Creutzig-Kanade-McRae, we can study its representation theory using this simple current extension. An analogous extension procedure for quantum groups was developed by Creutzig-Rupert. I will explain how to apply their strategy to U_q^H(sl(2)), the unrolled restricted quantum group at 4-th root of unity, and obtain a quantum supergroup whose category of representations is equivalent to that of V_B. This is joint work with T. Creutzig and T. Dimofte.