Groupes lin\'eaires finis permutant deux fois transitivement un ensemble de droites

TL;DR

This paper classifies linear group representations of doubly transitive groups that contain equiangular vector lines, and illustrates the construction for specific groups like SL_d(q) with odd q.

Contribution

It provides a complete classification of such representations for doubly transitive groups and demonstrates explicit examples for certain special linear groups.

Findings

Classified all linear representations with equiangular lines for doubly transitive groups.

Constructed explicit examples for G=SL_d(q) with q odd and d>1.

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.