Inequalities characterizing distinguished unipotent orbits

TL;DR

This paper introduces a new way to characterize distinguished unipotent orbits in reductive groups, using combinatorial methods for classical groups and computational checks for exceptional groups, aiding future work on cuspidal sheaves.

Contribution

It provides a novel characterization of distinguished unipotent orbits, combining combinatorial and computational approaches, essential for advancing the theory of cuspidal sheaves on L-parameter stacks.

Findings

New characterization of distinguished unipotent orbits

Combinatorial computation for classical groups

Computer verification for exceptional groups

Abstract

In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial computation, and for exceptional groups we check it with a computer. This characterization is needed in the theory of cuspidal sheaves on the stack of L-parameters in forthcoming work of the first two named authors.