Mathematische Zeitschrift

, Volume 267, Issue 1, pp 185–219

Support varieties, AR-components, and good filtrations


DOI: 10.1007/s00209-009-0616-6

Cite this article as:
Farnsteiner, R. & Röhrle, G. Math. Z. (2011) 267: 185. doi:10.1007/s00209-009-0616-6


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 GrT-modules, we determine the position of simple modules and baby Verma modules within the stable Auslander–Reiten quiver Γs(Gr) 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.

Mathematics Subject Classification (2000)

Primary 16G70 Secondary 17B50 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KielKielGermany
  2. 2.Department of MathematicsUniversity of BochumBochumGermany

Personalised recommendations