Polystability of Stokes representations and differential Galois groups

TL;DR

This paper characterizes the polystability of twisted Stokes representations through their differential Galois groups, extending classical results and establishing an intrinsic approach via Stokes local systems.

Contribution

It generalizes Richardson's results by linking polystability of wild monodromy representations to differential Galois groups and introduces an intrinsic reduction-based framework.

Findings

Polystability characterized by differential Galois groups.

Extension of Richardson's results to wild monodromy.

Intrinsic approach via reductions of Stokes local systems.

Abstract

Polystability of (twisted) Stokes representations (i.e. wild monodromy representations) will be characterised, in terms of the corresponding differential Galois group (generalising the Zariski closure of the monodromy group in the tame case). This extends some results of Richardson. Further, the intrinsic approach to such results will be established, in terms of reductions of Stokes local systems.