Representations of the Full Linear Group Over a Finite Field

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