Representations of finite sets and
                    correspondences

Bouc, Serge

doi:10.1090/conm/758/15231

Cited by 1 publication

(2 citation statements)

References 13 publications

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“…On the other hand, the opposite phenomenon can appear. In the context of correspondence functors recently developed by Bouc and Thévenaz (see [10] for lots of details ) every object of their category is generated by a larger object. So there is no non-trivial vanishing.…”

Section: There Existsmentioning

confidence: 99%

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Around evaluations of biset functors

Rognerud¹

2019

Annales De l'Institut Fourier

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The evaluation functor carries important information about the category of biset functors into the category of modules over the double Burnside algebra. Our purpose here, is to study double Burnside algebras via evaluations of biset functors. In order to avoid the difficult problem of vanishing of simple functors, we look at finite groups for which there is no non-trivial vanishing and we call them non-vanishing groups. This family contains all the abelian groups, but also infinitely many others. We show that for a non-vanishing group, there is an equivalence between the category of modules over the double Burnside algebra and a specific category of biset functors. Then, we deduce results about the highest-weight structure, and the self-injective property of the double Burnside algebra. We also revisit Barker's Theorem on the semi-simplicity of the category of biset functors.

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Section: There Existsmentioning

confidence: 99%

“…This question is not hopeless since the corresponding question has a positive answer for the category of finite sets with correspondences (See Lemma 4.1 of [10]). Question 5.6.…”

Section: The Group G Is S-self Dual If and Only If G Is Nilpotent And...mentioning

confidence: 99%

Around evaluations of biset functors

Rognerud¹

2019

Annales De l'Institut Fourier

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show abstract

Representations of finite sets and correspondences

Cited by 1 publication

References 13 publications

Around evaluations of biset functors

Around evaluations of biset functors

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