Classification of some Global Integrals related to groups of type $A_n$

TL;DR

This paper classifies specific global integrals related to groups of type A_n using unipotent orbits, establishing a dimension equation and conjecturing about their length, contributing to the understanding of their structure.

Contribution

It introduces a classification framework for global integrals of type A_n groups based on unipotent orbits and the dimension equation, and proposes a new conjecture on their length.

Findings

Classification of global integrals satisfying the dimension equation

Identification of which integrals are global unipotent integrals

A conjecture on the length of these integrals

Abstract

In this paper we start a classification of certain global integrals. First, we use the language of unipotent orbits to write down a family of global integrals. We then classify all those integrals which satisfy the dimension equation we set. After doing so, we check which of these integrals are global unipotent integrals. We do all this for groups of type $A_n$, and using all this we derive a certain interesting conjecture about the length of these integrals.