Stiefel Whitney classes for real representations of GL2(𝔽q)

Abstract

We compute the total Stiefel Whitney class for a real representation [Formula: see text] of [Formula: see text], where [Formula: see text] is odd. The obstruction class of [Formula: see text] is defined to be the Stiefel Whitney class of lowest positive degree that does not vanish. We provide an expression for the obstruction class of [Formula: see text] in terms of its character values if det [Formula: see text].