Equivalence of absolutely irreducible orthogonal representations of finite groups (Q1913971)

Let \(V\) be a finite dimensional vector space over a field \(K\) of characteristic \(\neq 2\), \(b:V\times V\to K\) a non-degenerate symmetric bilinear form and \(\rho:G\to O(b)\) be an orthogonal representation, absolutely irreducible as a linear representation, of the finite group \(G\). The author investigates the orthogonal equivalence of orthogonal representations \(\rho':G\to O(b')\) which are equivalent to \(\rho\) as linear representations, and characterizes the corresponding equivalence classes.