“A Filtration of the Rational Representation functor”

 

 

 

by

 

ERGÜN YARANERİ

(Bilkent University)

 

 

Abstract: The rational representation functor R assigns to each finite group G the abelian group R(G), which is the Grothendieck group of finite dimensional rational representations of  G with respect to exact sequences, and connects these modules via induction, restriction, inflation, deflation maps, satisfying several axioms, including the Mackey formula. We mainly consider kR on the class of all finite abelian p-groups where kR is obtained from R by extending the coefficients to a field k of characteristic p>0. We will explain an already known fact that kR is a uniserial functor and give its unique composition series. This will be achieved by using a filtration of the Burnside functor and using the well-known epimorphism from the Bunside ring to the rational representation ring.

 

 

 

 

 

 

 

Date : March 4, 2009 (Wednesday)

Time : 13:40-14:30

Place: Room SAZ01