The ring of equivariant vector bundles on finite sets
For any finite group \(G\) the author defines \(G\)-vector bundles associated with a finite dimensional representation of \(G\) over a field of characteristic \(p\). The author defines a Grothendieck group of vector bundles arising this way and a ring structure is defined on the Grothendieck group. Elaborating in this setting, the author gives a simple proof for an explicit Conlon-induction formula as is given in a more general form by \textit{R. Boltje} [Astérisque 181-182, 31-59 (1990; Zbl 0718.20005)]. The author gives a further application to species as in [\textit{D. J. Benson} and \textit{R. A. Parker}, J. Algebra 87, 290-331 (1984; Zbl 0539.20009)].
scientific article; zbMATH DE number 783922