Let G be a simple, simply
connected affine algebraic group over an algebraically closed field k of non-zero
characteristic p. We consider the problem of determining the extensions of
irreducible modules by irreducible modules. The extensions may be realized as
submodules of modules induced from characters on a Borel subgroup of G.
The geometry of the distribution of composition factors of those induced
modules is determined by an operation (namely, alcove transition) of the
Weyl group on the space of weights. Generically in the lowest p2-alcove,
that operation stabilizes a canonical subset of the set of highest weights of
those irreducible modules which extend the irreducible module of some fixed
highest weight. The stability leads to an upper bound on that subset, which
can be refined using the translation principle. We give a conjecture for the
generic distribution of extensions of irreducible modules by a fixed irreducible
module.
