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Pré-Publication, Document De Travail Année : 2009

On the Cartan matrix of Mackey algebras

Résumé

Let k be a field of characteristic p>0, and G be a finite group. The first result of this paper is an explicit formula for the determinant of the Cartan matrix of the Mackey algebra mu_k(G) of G over k. The second one is a formula for the rank of the Cartan matrix of the cohomological Mackey algebra comu_k(G) of G over k, and a characterization of the groups G for which this matrix is non singular. The third result is a generalization of this rank formula and characterization to blocks of comu_k(G) : in particular, if b is a block of kG, the Cartan matrix of the corresponding block comu_k(b) of comu_k(G) is non singular if and only if b is nilpotent with cyclic defect groups.
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Dates et versions

hal-00443661 , version 1 (02-01-2010)
hal-00443661 , version 2 (06-09-2010)

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Citer

Serge Bouc. On the Cartan matrix of Mackey algebras. 2009. ⟨hal-00443661v2⟩

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