We propose a conjectural construction of various slices for double affine Grass-
mannians as Coulomb branches of 3-dimensional N = 4 supersymmetric affine quiver
gauge theories. It generalizes the known construction for the usual affine Grassman-
nians, and makes sense for arbitrary symmetric Kac-Mody algebras.
We slightly extend results of Evens and Mirković and “compute” the characteristic cycles of intersection cohomology sheaves on transversal slices in a double affine Grassmannian. We propose a conjecture relating the hyperbolic stalks and microlocalization at a torus-fixed point in a Poisson variety. © 2015, Springer Science+Business Media New York.
This is the second paper of the series, started by Braverman-Finkelberg (2010) which describes a conjectural analogue of the affine Grassmannian for affine Kac-Moody groups (also known as double affine Grassmannian). The current paper is dedicated to describing a conjectural analogue of the convolution diagram for the double affine Grassmannian. In case our group is the special linear group, our conjectures can be derived from the work of Nakajima.