Quasi-Permutation Representations for the Borel and Maximal Parabolic Subgroups of

A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix.Thus every permutation matrix over C is a quasi-permutation matrix . The minimal degree of a faithful representation of G by quasi-permutation matrices over the complex numbers is denoted by ),(Gc and )(Gr denotes the minimal degree of a faithful rational valued complex character of )(Gr are calculated for the Borel or maximal parabolic subgroups of G . In this paper