English

Essential support of Green biset functors via morphisms

Representation Theory 2020-01-07 v1

Abstract

We present a very natural but yet useful criterion to detect vanishing of essential algebras of a Green biset functor AA by means of morphisms. We introduce the morphisms Inf:AAGInf:A \rightarrow A_G and Res:AGARes:A_G\rightarrow A to prove that the class of groups for which the essential algebras do not vanish is the same for AA and any shifted functor AGA_G. We use the kernel of ResRes to give a characterization of the seeds of simple AGA_G-modules which are not obtained as pullback of simple AA-modules.

Keywords

Cite

@article{arxiv.2001.00961,
  title  = {Essential support of Green biset functors via morphisms},
  author = {Benjamín García},
  journal= {arXiv preprint arXiv:2001.00961},
  year   = {2020}
}