eprintid: 15435
rev_number: 14
eprint_status: archive
userid: 780
dir: disk0/00/01/54/35
datestamp: 2013-08-20 12:20:11
lastmod: 2013-08-26 10:36:05
status_changed: 2013-08-20 12:20:11
type: doctoralThesis
metadata_visibility: show
creators_name: Heidersdorf, Thorsten
title: Pro-reductive groups attached to irreducible representations of the General Linear Supergroup
subjects: 500
subjects: 510
divisions: 110400
adv_faculty: af-11
keywords: Representations of the General Linear Supergroup, Tensor product decompositions, Deligne's category, Super-Tannakian categories
abstract: 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).
date: 2013
id_scheme: DOI
id_number: 10.11588/heidok.00015435
ppn_swb: 1652975780
own_urn: urn:nbn:de:bsz:16-heidok-154356
date_accepted: 2013-07-25
advisor: HASH(0x564e1c52f8c0)
language: eng
bibsort: HEIDERSDORPROREDUCTI2013
full_text_status: public
citation:   Heidersdorf, Thorsten  (2013) Pro-reductive groups attached to irreducible representations of the General Linear Supergroup.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/15435/1/phd-main.pdf