Group Representation Theory

2016 ◽  
pp. 21-67
Author(s):  
Masahito Hayashi
Keyword(s):  
Representation Theory ◽  
Group Representation ◽  
Group Representation Theory

scholarly journals Stratifications and Mackey Functors II: Globally Defined Mackey Functors

2010 ◽  
Vol 6 (1) ◽  
pp. 99-170 ◽  
Author(s):  
Peter Webb
Keyword(s):  
Representation Theory ◽  
Structural Properties ◽  
Characteristic Zero ◽  
Group Representation ◽  
Cartan Matrix ◽  
Weight Category ◽  
Group Representation Theory ◽  
Stratification Theory ◽  
Highest Weight ◽  
Mackey Functors

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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