Stiefel-Whitney Classes of Representations of $\text{SL}(2,q)$

We describe the Stiefel-Whitney classes (SWCs) of orthogonal representations $π$ of the finite special linear groups $G=\text{SL}(2,\mathbb F_q)$, in terms of character values of $π$. From this calculation, we can answer interesting questions about SWCs of $π$. For instance, we determine the subalgebra of $H^*(G,\mathbb Z/2\mathbb Z)$ generated by the SWCs of orthogonal $π$, and we also determine which $π$ have nontrivial mod $2$ Euler class.

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