  Let G be a connected and reductive algebraic group over an algebraically
closed field of characteristic p > 0. An interesting class of representations
of G consists of those G-modules having a good filtration -- i.e. a filtration
whose layers are the standard highest weight modules obtained as the space of
global sections of G-linearized line bundles on the flag variety of G. Let H be
a connected and reductive subgroup of G. One says that (G,H) is a Donkin pair,
or that H is a good filtration subgroup of G, if every G-module with good
filtration also has a good filtration as an H-module.
  In this paper, we show when G is a "classical group" that the optimal
SL2-subgroups of G are good filtration subgroups, and we also determine some
primes for which distinguished optimal SL2-subgroups of groups of exceptional
type are good filtration subgroups. Additionally, we consider the cases of
subsystem subgroups in all types and determine some primes for which they are
good filtration subgroups.

Representation Theory