An Irregular Deligne–Simpson Problem

The Deligne--Simpson problem asks for a criterion of the existence of connections on an algebraic curve with prescribed singularities at punctures. We give a solution to a generalization of this problem to $G$-connections on $\mathbb{P}^1$ with a regular singularity and an irregular singularity (satisfying a condition called isoclinic). Here $G$ can be any complex reductive group. Perhaps surprisingly, the solution can be expressed in terms of representations of rational Cherednik algebras. This is joint work with Konstantin Jakob.