Groupes linéaires finis permutant deux fois transitivement un ensemble de droites

Abstract

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.