Introduction. In this paper it is proved that the irreducible projective representations of the group G of automorphisms of a Lie algebra of classical type constructed in [2] remain irreducible and inequivalent when restricted to the subgroup Go of G generated by the oneparameter subgroups { exp(adiea) } where a ranges over the set of roots of V with respect to a fixed Cartan subalgebra, and t is taken from the prime field Qo in U. The proofs of irreducibility and inequivalence given in [2] apply without change to Go in case Qo is infinite, so there is no problem unless Qo is the prime field of p elements for a prime p>0, and in this case an entirely different argument seems to be required.2 When Qo is finite, the group Go is finite, and can be identified at least in certain cases with one of the finite linear groups introduced by Chevalley [1]. The results of this paper exhibit a family of irreducible projective representations of these groups, while in another paper [3 ], some results on the degrees of these representations are obtained.3 The next problem to be investigated in this connection is whether the representations obtained in this paper give all the irreducible projective representations of the groups Go.