Modular representations and monomial burnside rings

Abstract

We introduce canonical induction formulae for some character rings of a finite group, some of which follows from the formula for the complex character ring constructed by Boltje. The rings we will investigate are the ring of modular characters, the ring of characters over a number field, in particular, the field of real numbers and the ring of rational characters of a finite p−group. We also find the image of primitive idempotents of the algebra of the complex and modular character rings under the corresponding canonical induction formulae. The thesis also contains a summary of the theory of the canonical induction formula and a review of the induction theorems that are used to construct the formulae mentioned above.