Euphotic representations and rigid automorphic data

TL;DR

This paper introduces a novel method for constructing rigid automorphic representations and local systems for reductive groups, utilizing euphotic representations and Hessenberg varieties to establish rigidity.

Contribution

It presents the concept of euphotic representations and links geometric structures to the construction of rigid automorphic data, advancing the understanding of rigidity in automorphic forms.

Findings

Established a new construction method for rigid automorphic representations.

Connected Hessenberg varieties to the proof of rigidity.

Introduced euphotic representations as a key tool.

Abstract

We propose a new method to construct rigid $G$-automorphic representations and rigid $\widehat{G}$-local systems for reductive groups $G$. The construction involves the notion of euphotic representations, and the proof for rigidity involves the geometry of certain Hessenberg varieties.