Generic Representation Theory of the Additive and Heisenberg Groups
arXiv:1011.0509
Abstract
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.
This paper is being withdrawn because I recently discovered that almost half of the results contained therein are already known, and I do not wish to have them attributed to me. I plan on submitting an updated version of this paper, with proper citations