Generic Representation Theory of the Additive and Heisenberg Groups
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.
Keywords
Cite
@article{arxiv.1011.0509,
title = {Generic Representation Theory of the Additive and Heisenberg Groups},
author = {Michael Crumley},
journal= {arXiv preprint arXiv:1011.0509},
year = {2011}
}
Comments
This paper is being withdrawn because I recently discovered that almost half of the results contained therein are already known, and I do not wish to have them attributed to me.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