Stiefel-Whitney Classes for finite special linear groups of even rank

Abstract

We compute the total Stiefel-Whitney Classes (SWCs) for orthogonal representations of special linear groups when n and q are odd. These classes are expressed in terms of character values at diagonal elements of order 2. We give several consequences, and work out the 4th SWC explicitly, and the 8th SWC when the 4th vanishes.