caa a22 4500 445836296 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00209-009-0616-6 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0616-6 Support varieties, AR-components, and good filtrations [Elektronische Daten] [Rolf Farnsteiner, Gerhard Röhrle] Let G be a reductive group, defined over the Galois field $${\mathbb{F}_p}$$ with p being good for G. Using support varieties and covering techniques based on G r T-modules, we determine the position of simple modules and baby Verma modules within the stable Auslander-Reiten quiver Γs(G r) of the rth Frobenius kernel of G. In particular, we show that the almost split sequences terminating in these modules usually have an indecomposable middle term. Concerning support varieties, we introduce a reduction technique leading to isomorphisms$$\mathcal{V}_{G_r}(Z_r(\lambda)) \cong \mathcal{V}_{G_{r-d}}(Z_{r-d}(\mu))$$for baby Verma modules of certain highest weights $${\lambda, \mu \in X(T)}$$, which are related by the notion of depth. Springer-Verlag, 2009 Farnsteiner Rolf Department of Mathematics, University of Kiel, Ludewig-Meyn-Str. 4, 24098, Kiel, Germany aut Röhrle Gerhard Department of Mathematics, University of Bochum, 44780, Bochum, Germany aut Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 185-219 0025-5874 267:1-2<185 2011 267 209 https://doi.org/10.1007/s00209-009-0616-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0616-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Farnsteiner Rolf Department of Mathematics, University of Kiel, Ludewig-Meyn-Str. 4, 24098, Kiel, Germany aut NATIONALLICENCE 700 1- Röhrle Gerhard Department of Mathematics, University of Bochum, 44780, Bochum, Germany aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 185-219 0025-5874 267:1-2<185 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer