Mathematische Zeitschrift

, Volume 267, Issue 1, pp 185–219

Support varieties, AR-components, and good filtrations

Authors

    • Department of MathematicsUniversity of Kiel
  • Gerhard Röhrle
    • Department of MathematicsUniversity of Bochum
Article

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
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Abstract

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 16G70Secondary 17B50

Copyright information

© Springer-Verlag 2009