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.



Massachusetts Institute of Technology