Elliptic Weyl group elements and unipotent isometries with p=2

TL;DR

This paper characterizes unipotent conjugacy classes in classical groups over fields of characteristic 2 using elliptic Weyl group elements, extending known results from odd characteristic and exceptional groups.

Contribution

It provides a new characterization of unipotent classes in characteristic 2 via closure relations, generalizing previous results to classical groups.

Findings

Unipotent classes are characterized by closure relations.

Extension of known results from odd characteristic to characteristic 2.

Connections between elliptic Weyl group elements and unipotent classes.

Abstract

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class \Phi(C) in G. In this paper we show that \Phi(C) can be characterized in terms of the closure relations between unipotent classes. Previously the analogous result was known in odd characteristic and for exceptional groups in any characteristic.