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

TL;DR

This paper calculates the number of degree n representations and the dimensions of invariant bilinear forms for groups of order p^3, with p an odd prime, highlighting their relevance in physical sciences.

Contribution

It provides explicit computations of representation counts and invariant bilinear form dimensions for p^3 order groups, including conditions for non-degeneracy.

Findings

Number of n degree representations computed

Dimensions of invariant bilinear forms determined

Existence conditions for non-degenerate forms established

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.