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 newline newline