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Stratifications and Mackey Functors II: Globally Defined Mackey Functors
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AbstractWe 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.
Title: Stratifications and Mackey Functors II: Globally Defined Mackey Functors
Description:
AbstractWe 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.
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