Algebra and Geometry Seminar

There are two major predictions for the quantum K-ring of a partial flag: One comes from quantum field theory, where the ring is the OPE ring associated to a 3D GLSM. The other comes from work identifying the quasimap version of the ring with the Bethe algebra associated to a quantum integrable system. These predictions have a mysterious set of equations in common, which can be regarded as a special case of Nekrasov-Shatashvili's gauge/Bethe correspondence. We give a purely geometric explanation for this coincidence in terms of the abelian/non-abelian correspondence and use it to prove both sets of predictions.