It is generally believed (and for the most part is probably true) that Lie
theory, in contrast to the characteristic zero case, is insufficient to tackle
the representation theory of algebraic groups over prime characteristic fields.
However, in this paper we show that, for a large and important class of
unipotent algebraic groups (namely the unipotent upper triangular groups
$U_n$), and under a certain hypothesis relating the characteristic $p$ to both
$n$ and the dimension $d$ of a representation (specifically, $p \geq
\text{max}(n,2d)$), Lie theory is completely sufficient to determine the
representation theory of these groups. To finish, we mention some important
analogies (both functorial and cohomological) between the characteristic zero
theories of these groups and their `generic' representation theory in
characteristic $p$.