Geometric Langlands correspondence for SL(2), PGL(2) over the pair of pants

TL;DR

This paper proves the Geometric Langlands correspondence for rank one groups over a thrice-punctured projective line, advancing understanding of the relationship between automorphic forms and Galois representations in this specific setting.

Contribution

It establishes the Geometric Langlands correspondence for SL(2) and PGL(2) over the pair of pants, a case with three tame ramification points, which was previously unresolved.

Findings

Confirmed the correspondence for SL(2) and PGL(2) over the thrice-punctured projective line.

Provided explicit constructions of automorphic and Galois data in this setting.

Extended the scope of the geometric Langlands program to new ramification configurations.

Abstract

We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.