  Let $\mathfrak{g}$ be a reductive Lie algebra and let
$\vec{V}(\vec{\lambda})$ be a tensor product of $k$ copies of finite
dimensional irreducible $\mathfrak{g}$-modules. Choosing $k$ points in
$\mathbb{C}$, $\vec{V}(\vec{\lambda})$ acquires a natural structure of the
current algebra $\mathfrak{g}\otimes \mathbb{C}[t]$-module. Following a work of
Rao [R], we produce an explicit and complete set of $\mathfrak{g}$-module
intertwiners of $\vec{V}(\vec{\lambda})$ in terms of the action of the current
algebra.

Representation Theory