Study of antiorbital complexes

TL;DR

This paper investigates special complexes of l-adic sheaves called biorbital complexes, focusing on their properties and examples within the context of eigenspaces of semisimple automorphisms of reductive Lie algebras.

Contribution

It introduces the concept of biorbital complexes and studies their examples in the setting of eigenspaces of semisimple automorphisms, expanding understanding of orbital sheaves.

Findings

Identification of biorbital complexes in specific algebraic settings

Examples of biorbital complexes related to eigenspaces of automorphisms

Insights into the structure of orbital and biorbital sheaves

Abstract

Let E be a finite dimensional vector space over an algebraic closure of a finite field with a given linear action of a connected linear algebraic group K and let E' be the dual space. A complex of l-adic sheaves on E is said to be orbital if it is a simple perverse sheaf whose support is a single K-orbit. A complex of l-adic sheaves on E is said to be biorbital if it is orbital and if its Deligne Fourier transform is orbital on E'. In this paper we study examples of biorbital complexes arising in the case where E is an eigenspace of a semisimple automorphism of a reductive Lie algebra.