Elliptic Weyl group elements and unipotent isometries with $p=2$

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 $\Phi (C)$ of $G$. 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.