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We give a provisional construction of the Kac-Moody Lie algebra modulestructure on the hyperbolic restriction of the intersection cohomology complexof the Coulomb branch of a framed quiver gauge theory, as a refinement of theconjectural geometric Satake correspondence for Kac-Moody algebras proposed inan earlier paper with Braverman, Finkelberg in 2019. This construction assumesseveral geometric properties of the Coulomb branch under the torus action.These properties are checked in affine type A, via the identification of theCoulomb branch with a Cherkis bow variety established in a joint work withTakayama.

Towards geometric Satake correspondence for Kac-Moody algebras -- Cherkis bow varieties and affine Lie algebras of type $A$