
PDF, English
 main document
Download (992kB)  Terms of use 
Abstract
We study tensor product decompositions of representations of the General Linear Supergroup Gl(mn). We show that the quotient of Rep(Gl(mn),\epsilon)$ by the tensor ideal of negligible representations is the representation category of a proreductive supergroup G red. In the Gl(m1)case we show G red = Gl(m1) \times Gl(1) \times Gl(1). In the general case we study the image of the canonical tensor functor Fmn from Deligne's interpolating category Rep (Gl mn) to Rep(Gl(mn),\epsilon). We determine the image of indecomposable elements under Fmn. This implies tensor product decompositions between projective modules and between certain irreducible modules, including all irreducible representations in the Gl(m1)case. Using techniques from Deligne's category we derive a closed formula for the tensor product of two maximally atypical irreducible Gl(22)representations. We study cohomological tensor functors DS : Rep(Gl(mm), epsilon) > Rep(Gl(m1m1)) and describe the image of an irreducible element under DS. At the end we explain how these results can be used to determine the proreductive group G L \hookrightarrow Gl(mm) red corresponding to the subcategory Rep(G L, epsilon) generated by the image of an irreducible element L in Rep(Gl(mm) red, epsilon).
Item Type:  Dissertation 

Supervisor:  Weissauer, Prof. Dr. Rainer 
Date of thesis defense:  25 July 2013 
Date Deposited:  20 Aug 2013 12:20 
Date:  2013 
Faculties / Institutes:  The Faculty of Mathematics and Computer Science > Department of Mathematics 
Subjects:  500 Natural sciences and mathematics 510 Mathematics 
Uncontrolled Keywords:  Representations of the General Linear Supergroup, Tensor product decompositions, Deligne's category, SuperTannakian categories 