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Restricted Determinantal Homomorphisms and Locally Free Class Groups

Let K be a number field and let OK denote the integers of K. The locally free class groups, Cl(OK [G]), furnish a fundamental collection of invariants of a finite group, G. In this paper I will construct some new, non-trivial homomorphisms, called restricted determinants, which map the NGH-invariant idèlic units of Ok([Hab] to Cl(OK [G]). These homomorphisms are constructed by means of the Horn-description of Cl(OK [G]), which describes the locally free class group in terms of the representation theory of G, and the technique of Explicit Brauer Induction, which was introduced in [5].