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

Abstract

Orthogonal representations \pi of a finite group G have invariants w_i(\pi), living in the ith degree cohomology group H^i(G, Z/2Z), called Stiefel-Whitney Classes (SWCs). Their sum is known as the total SWC of \pi. There do not seem to have many explicit calculations in the literature of SWCs for the non-abelian groups. In this thesis we present the total SWCs for orthogonal representations of several finite groups of Lie type, namely symplectic groups Sp(2n,q) and special linear groups SL(2n+1,q) when q is odd. We also describe the SWCs for SL(2,q) for even q.