Title: Polynomially and Infinitesimally Injective Modules,
Abstract: The injective polynomial modules for a general linear group $G$ of degree $n$
are labelled by the partitions with at most $n$ parts. Working over an
algebraically closed field of characteristic $p$, we consider the question of
which partitions correspond to polynomially injective modules that are also
injective as modules for the restricted enveloping algebra of the Lie algebra
of $G$. The question is related to the "index of divisibility" of a polynomial
module in general, and an explicit answer is given for $n=2$.