Invariant bilinear forms under the operator group of order p^3 with odd prime p

Abstract

In this paper we compute the number of n degree representations of a group of order p^3 for p an odd prime and the dimensions of corresponding spaces of invariant bilinear forms over an algebraically closed field F. We explicitly discuss about the existence of non-degenerate invariant bilinear forms. The results are important due to their application in the studies of physical sciences.

Submitted for kind consideration. arXiv admin note: substantial text overlap with arXiv:1910.09850