Induction formulae for Mackey functors with applications to representations of the twisted quantum double of a finite group

Abstract

In the theory of canonical induction formulae for Mackey functors, Boltje [4] demonstrated that the plus constructions, together with the mark morphism, are useful for the study of canonical versions of induction theorems analogous to those in representation theory of finite groups. In this paper, we present a short exact sequence for the plus constructions derived from Cauchy–Frobenius lemma, and apply it to the proof of Boltje's integrality result for canonical induction formulae. The methods appearing in Boltje's theory, combined with the Dress construction for Mackey functors, are applicable to induction theorems on representations of the twisted quantum double of a finite group. As a sequel to such a research, we describe canonical versions of two induction theorems whose origins are Artin's induction theorem and Brauer's induction theorem on C-characters of a finite group.