Quasi -permutation representations of special orthogonal groups

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. For a given finite group G, the minimal degree of a faithful permutation representation by quasi-permutation matrices over the rational and the complex numbers are denoted by Gq and Gc respectively. Finally, Gr denotes the minimal degree of a faithful rational valued complex character of G. In this paper, we will calculate Gq, Gc and Gr for the special orthogonal groups.

Quasi -permutation representations of special orthogonal groups Keywords:

Character table , Quasi-permutation representation , Orthogonal group , Special orthogonal group , Rational value character