COMPLEX REPRESENTATIONS OF GLn(Fq)

This paper seeks to examine the representations of GLn(Fq) for n \u3e 1, q = pk for some prime p and integer k. This family of groups provides a useful first example when examining the classication of group representations for a group G. The non-cuspidal representations of GL2(Fq) and GL3(Fq) will be explicitly constructed, with a short discussion on the generalization of these constructions to the more general case, GLn(Fq)