TY  - GEN
A1  - Heidersdorf, Thorsten
N2  - We study tensor product decompositions of representations of the General Linear Supergroup Gl(m|n). We show that the quotient of Rep(Gl(m|n),\epsilon)$ by the tensor ideal of negligible representations is the representation category of a pro-reductive supergroup G red. In the Gl(m|1)-case we show G red = Gl(m-1) \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 m-n) to Rep(Gl(m|n),\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(m|1)-case. Using techniques from Deligne's category we derive a closed formula for the tensor product of two maximally atypical irreducible Gl(2|2)-representations. We study cohomological tensor functors DS : Rep(Gl(m|m), epsilon) -> Rep(Gl(m-1|m-1)) and describe the image of an irreducible element under DS. At the end we explain how these results can be used to determine the pro-reductive group G L \hookrightarrow Gl(m|m) red corresponding to the subcategory Rep(G L, epsilon) generated by the image of an irreducible element L in Rep(Gl(m|m) red, epsilon).
KW  - Representations of the General Linear Supergroup
KW  -  Tensor product decompositions
KW  -  Deligne's category
KW  -  Super-Tannakian categories
AV  - public
TI  - Pro-reductive groups attached to irreducible representations of the General Linear Supergroup
Y1  - 2013///
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/15435/
ID  - heidok15435
ER  -