  We study structural properties of truncated Weyl modules. A truncated Weyl
module $W_N(\lambda)$ is a local Weyl module for $\mathfrak g[t]_N = \mathfrak
g \otimes \frac{\mathbb C[t]}{t^N\mathbb C[t]}$, where $\mathfrak g$ is a
finite-dimensional simple Lie algebra. It has been conjectured that, if $N$ is
sufficiently small with respect to $\lambda$, the truncated Weyl module is
isomorphic to a fusion product of certain irreducible modules. Our main result
proves this conjecture when $\lambda$ is a multiple of certain fundamental
weights, including all minuscule ones for simply laced $\mathfrak g$. We also
take a further step towards proving the conjecture for all multiples of
fundamental weights by proving that the corresponding truncated Weyl module is
isomorphic to a natural quotient of a fusion product of Kirillov-Reshetikhin
modules. One important part of the proof of the main result shows that any
truncated Weyl module is isomorphic to a Chari-Venkatesh module and explicitly
describes the corresponding family of partitions. This leads to further results
in the case that $\mathfrak g=\mathfrak{sl}_2$ related to Demazure flags and
chains of inclusions of truncated Weyl modules.
