Invariant bilinear forms under the rigid motions of a regular polygon

Abstract: In this paper, for n a positve integer, we compute the number of n degree representations for a dihedral group G of order 2m, m \geq 3 and the dimensions of the corresponding spaces of G invariant bilinear forms over a complex field C. We explicitly discuss about the existence of a non-degenerate invariant bilinear form. The results are important due to their applications in the studies of physical sciences.