Stiefel-Whitney Classes of Representations of Some Finite Groups of Lie Type

TL;DR

This paper computes the Stiefel-Whitney classes for orthogonal representations of specific finite groups of Lie type, expanding understanding of their topological invariants in algebraic and geometric contexts.

Contribution

It provides explicit calculations of Stiefel-Whitney classes for orthogonal representations of several finite groups of Lie type, including cases for both odd and even q.

Findings

Stiefel-Whitney classes for SL(2,q), SL(3,q), Sp(4,q), Sp(6,q) with q odd

Descriptions of SWCs for SL(2,q) with q even

Enhanced understanding of topological invariants of finite groups of Lie type

Abstract

In this note we present the Stiefel-Whitney classes (SWCs) for orthogonal representations of several finite groups of Lie type, namely for $G=\text{SL}(2,q),$ $\text{SL}(3,q),$ $\text{Sp}(4,q)$, and $\text{Sp}(6,q)$, with $q$ odd. We also describe the SWCs for $G=\text{SL}(2,q)$ when $q$ is even.