Effective equivalence of orthogonal representations of finite groups (Q1373210)

[For undefined notions see the preceding review Zbl 0956.20003.] From the introduction: Our principal goal is to provide effective means of distinguishing equivalence classes of orthogonal representations in certain cases by using a combination of methods which are already known in some form or other, but usually not in a form useful for explicit calculations. The procedure is described in detail in Section 4. The most important of these methods is the Hermitian Morita theory which was introduced by \textit{A. Fröhlich} and \textit{A. M. McEvett} [J. Algebra 12, 79-104 (1969; Zbl 0256.15017)] as one of the critical steps in determining the Grothendieck and Witt groups of orthogonal representations. We shall make the correspondence provided by this theory explicit, and show how the formulas obtained can be used to determine whether or not two orthogonal representations are equivalent in the case when all (linearly) irreducible representations involved in them of ``class 1'' (cf. Section 3) are absolutely irreducible. An example of \(G\) the symmetric group \(S_4\) is given in Section 4. In Section 3, we record some facts which are useful in the context of orthogonal representations; again most are known but not all are explicit in the literature.