Quasi-permutation representations ofSL(2,q) and PSL(2,q)

Abstract

By a quasi-permutation matrix we meana square matrix over the complex field [Copf] with non-negative integraltrace. Thus every permutation matrix over [Copf] is a quasi-permutationmatrix. For a given finite group G, let p(G) denote the minimal degreeof a faithful permutation representation of G (or a faithfulrepresentation of G by permutation matrices), let q(G) denote theminimal degree of a faithful representation of G by quasi-permutationmatrices over the rational field ℚ, and let c(G) be the minimaldegree of a faithful representation of G by complex quasi-permutationmatrices. See [1].