Essential support of Green biset functors via morphisms

2020/01/03 by García, Benjamín
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/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 Inf:A → A_G and Res:A_G→ 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 Res to give a characterization of the seeds of simple A_G-modules which are not obtained as pullback of simple A-modules.

Related

• Simple modules over Green biset functors
• Vanishing evaluations of simple functors
• Around evaluations of biset functors
• Anti-involutions on Green biset functors
• Ideals of some Green biset functors