Authors : H.S. Ndakwo
Abstract: Let A(x) be the representation of an element x in a group G. The representation A(x) may be real or complex. The aim of this study is to distinguish when the character of A(x) is real and when it is not. This distinction is linked with the notion of bilinear invariants and to find out the situation in which if A(x) is complex for some x whether it is equivalent as a representation to Q(x) such that Q(x) has a real coefficients for all xG. This notion is equivalent to finding an invertible matrix T such that Q(x) = TA(x) T and Q(x) is real. It was also proved in this study that for any complex irreducible orthogonal representation of a finite group G, the representation Q(x) for every xG is equivalent to a real orthogonal representation.
H.S. Ndakwo , 2007. The Representation of Real Characters of Finite Groups . Research Journal of Applied Sciences, 2: 372-376.