Author: Peter Webb
Address:
School of Mathematics,
University of Minnesota,
Minneapolis MN 55455

Title:
Stratifications and Mackey Functors II: Globally Defined Mackey Functors

Abstract:
We describe structural properties of globally defined Mackey functors related to the stratification 
theory of algebras. We show that over a field of characteristic zero they form a highest weight 
category and we also determine precisely when this category is semisimple. This approach is used to 
show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite 
parts of it in some instances. We also develop a theory of vertices of globally defined Mackey 
functors in the spirit of group representation theory, as well as giving information about 
extensions between simple functors.

Preprint May 2008.