Author: Peter Webb
email: webb@math.umn.edu
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.