Representations of the full linear group over a finite field

Complex representations of the group $GL(n,\mathbf F_q)$ are studied, where $\mathbf F_q$ is a field of order $q$. The concept of analytic representations of $GL(n,\mathbf F_q)$ is introduced and is used to construct all the irreducible representations of $GL(n,\mathbf F_q)$. Results are obtained on the irreducible polynomials of 3rd degree over $\mathbf F_q$.
Bibliography: 21 titles.