Total Stiefel Whitney classes for real representations of ${\mathrm{GL}}_n$ over ${\mathbb{F}}_q,\mathbb{R}$ and $\mathbb{C}$

Jyotirmoy Ganguly, Rohit Joshi

We compute the total Stiefel Whitney class for a real representation $\pi$ of ${\mathrm{GL}}_n({\mathbb{F}}_q)$, where $q$ is odd in terms of character values of $\pi$ on order $2$ diagona…