Two-parameter Langlands Correspondence

Abstract

In our paper arXiv:1701.03146 we established, for every simply-laced Lie algebra g, a canonical isomorphism between the spaces of deformed conformal blocks of the deformed W-algebra and the quantum affine algebra corresponding to g, which we view as a q-deformation of the quantum Langlands correspondence. This was done by realizing the deformed conformal blocks of these algebras via the quantum K-theory of the Nakajima quiver varieties. We also linked this isomorphism to a duality emerging from the 6d little string theory. Here, we give a brief survey of these results and propose an extension to the non-simply laced case, which exhibits a Langlands-type duality.