Essential support of Green biset functors via morphisms

Benjamín García

paper

Essential support of Green biset functors via morphisms

arXiv:2001.00961

Abstract

We present a very natural but yet useful criterion to detect vanishing of essential algebras of a Green biset functor $A$ by means of morphisms. We introduce the morphisms $I n f : A \to A_{G}$ and $R es : A_{G} \to A$ to prove that the class of groups for which the essential algebras do not vanish is the same for $A$ and any shifted functor $A_{G}$ . We use the kernel of $R es$ to give a characterization of the seeds of simple $A_{G}$ -modules which are not obtained as pullback of simple $A$ -modules.