(G,P)-opers and global Slodowy slices

TL;DR

This paper generalizes G-opers to arbitrary parabolic subgroups, introduces a parameterization for (G,P)-opers, and connects these to higher Teichmuller spaces, expanding the understanding of Hitchin fibrations.

Contribution

It introduces (G,P)-opers for any parabolic subgroup and links them to higher Teichmuller spaces, broadening the scope of opers and Hitchin fibration analysis.

Findings

Parameterization of (G,P)-opers for even nilpotent parabolics.

Connection of (G,P)-opers to higher Teichmuller spaces.

Generalization of base of Hitchin fibration.

Abstract

In this paper, we introduce a generalization of G-opers for arbitrary parabolic subgroups P<G. For parabolic subgroups associated to even nilpotents, we parameterize (G,P)-opers by an object generalizing the base of the Hitchin fibration. In particular, we describe families of opers associated to higher Teichmuller spaces.