Browsing by Subject "Canonical induction"

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    Canonical induction for trivial source rings
    (2013) Büyükçolak, Yasemin
    We discuss the canonical induction formula for some special Mackey functors by following the construction of Boltje. These functors are the ordinary and modular character rings and the trivial source rings. Making use of a natural correspondence between the Mackey algebra and the finite algebra spanned by the three kinds of basic bisets, namely the conjugation, restriction and induction, we investigate the canonical induction formula in terms of the theory of bisets. We focus on the trivial source rings and the canonical induction formula for them. The main aim is to get an explicit formula for the canonical induction of regular bimodules in the trivial source. This gives a first step towards for the canonical induction of blocks.
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    Modular representations and monomial burnside rings
    (2004) Coşkun, Olcay
    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.