  In this paper we give an intimate connection between the characteristic zero
representation theories of the Additive and Heisenberg groups, and their
characteristic p >0 theories when p is much larger than the dimension a
representation. In particular, if p >> dimension, then all characteristic p
representations for these groups can be factored into commuting products of
representations, with each factor arising from a representation of the Lie
algebra of the group, one for each of the representation's Frobenius layers. In
this sense, for a fixed dimension and large enough p, all representations for
these groups look generically like representations for direct powers of
themselves over a field of characteristic zero.

Representation Theory