Mackey functors and fusion systems

Abstract

In this thesis, we present a survey for the paper [1]. We study with the biset functors representation rings and superclass functions. We define representation rings of a saturated fusion system F and F-stable elements of superclass functions, then, we investigate the dimension homomorphism between those sets. We consider arbitrary saturated fusion system F and finite group G. Our aim is to describe the image of the F-stable elements of real representation ring of G, under the dimension function which is the set of Borel-Smith functions which satisfy an extra condition.