  In this paper, we introduce a family of indecomposable finite--dimensional
graded modules for the current algebra associated to a simple Lie algebra.
These modules are indexed by a tuple of partitions one for each positive root
of the simple Lie algebra. We assume that the partitions satisfy a natural
compatibility condition. In the case when the partitions are all rectangular,
for instance, we prove that these are precisely the Demazure modules which are
stable under the action of the simple Lie algebra. As a consequence we see that
the defining relations of these Demazure modules can be greatly simplified. We
use this simplified presentation to relate our results to the fusion products
(defined by Feigin and Loktev) of representations of the current algebra. We
prove that the Q--system can be actually thought of as a canonical short exact
of the fusion products of representations associated to certain special
partitions. Finally, in the last section we deal with the case of sl(2) and
prove that the modules we define are just fusion products of irreducible
representations of the associated current algebra. We also give monomial bases
for these modules.
