Substrata in reductive groups

TL;DR

This paper introduces a new partitioning method for reductive groups into substrata, refining existing stratifications, and explores their properties through conjectures and examples.

Contribution

It defines substrata within reductive groups, proposes conjectural properties, and verifies these properties in specific examples, advancing understanding of group structure.

Findings

Partition of reductive groups into finitely many substrata

Conjectural properties of substrata proposed

Verification of properties in selected examples

Abstract

We define a partition of a reductive group into finitely many subsets, refining the partition of the group into strata. We state some conjectural properties of these subsets (called substrata) and verify them in some examples.