Nilpotent orbits in classical Lie algebras over $\textbf{F}_{2^n}$ and the Springer correspondence

TL;DR

This paper counts nilpotent orbits in classical Lie algebras over finite fields of characteristic 2 and constructs the Springer correspondence for these nilpotent varieties, advancing understanding in modular representation theory.

Contribution

It provides explicit counts of nilpotent orbits over $ extbf{F}_{2^n}$ and establishes the Springer correspondence in characteristic 2 for types B, C, and D.

Findings

Number of nilpotent orbits in orthogonal Lie algebras over $ extbf{F}_{2^n}$

Construction of Springer correspondence in characteristic 2

Extension of classical theory to modular setting

Abstract

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over $\tF_{2^n}$. Let $G$ be an adjoint algebraic group of type $B,C$ or $D$ defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the Lie algebra of $G$.