  Let n >1 be an integer, and G a doubly transitive subgroup of the symmetric
group on X={1,...,n}. In this paper we find all linear group representations
rho of G on an euclidean vector space V which contains a set of equiangular
vector lines GG={< v_1>,...,} such that : (1) V is generated by v_1,...,v_n,
(2) for all i in X and all g in G, = . Then we illustrate our construction when
G=SL_d(q), q odd and d > 1.
