MINIMAL CHARACTERS OF THE FINITE CLASSICAL-GROUPS

Let G(q) be a finite simple group of Lie type over a finite field of o rder q and d(G(q)) the minimal degree of faithful projective complex r epresentations of G(q). For the case G(q) is a classical group we dete rmine the number of projective complex characters of G(q) of degree d( G(q)). In several cases we also determine the projective complex chara cters of the second and the third lowest degrees. As a corollary of th ese results we deduce the classification of quasi-simple irreducible c omplex linear groups of degree at most 2r, r a prime divisor of the gr oup order.