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Stratifications and Mackey Functors II: Globally Defined Mackey Functors

Published online by Cambridge University Press:  02 February 2010

Peter Webb
Peter Webb
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA, webb@math.umn.edu
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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.

Keywords

Mackey functorbisetstratificationBurnside ringhighest weight category

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Type
Research Article
Information
Journal of K-Theory , Volume 6 , Issue 1 , August 2010, pp. 99 - 170
Copyright
Copyright © ISOPP 2010

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