On the ideals and essential algebras of shifted functors of linear representations

We present a study on the shifted Green biset functors kR(F,G) of linear F-representations with coefficients over k, for fields k and F of characteristic zero and a finite group G. We provide a criterion for the vanishing of their essential algebras and we prove that the condition of uniqueness of minimal groups for simple modules holds for these functors. We give a parametrization of a family of simple kR(Q,G)-modules. We also prove the semisimplicity of the category of CRC,G-modules by means of an equivalence with a category of modules over a semisimple algebra. (C) 2018 Elsevier Inc. All rights reserved.