the study of the finite-dimensional modules of these algebras, there are certain special modules, called Kirillov-Reshetikhin (KR) modules [@KR]. These can be defined in terms of their Drinfeld polynomials [@ChariPres], for example, which have a particularly simple form for these modules.

The modules are parameterized by ${{\mathfrak{g}}}$-highest weights of the form $k
\omega_{{\alpha}}$, that is, a multiple of one of the fundamental weights, as well as a complex parameter $\zeta$. We refer to such a module by $W_{{{\alpha}},k}(\zeta)$ where ${{\alpha}}\in I_r$, $k\in {{\mathbb Z}}_+$ and $\zeta\in
{{\mathbb C}}^*$. These are finite-dimensional modules, which are analogs of evaluation modules of affine algebras, which are obtained from inducing from the irreducible representation of the finite-dimensional subalgebra ${{\mathfrak{g}}}$, which does not depend on $\zeta$. Unlike such evaluation modules, however, they are not necessarily irreducible when restricted to the subalgebra $U_q({{\mathfrak{g}}})\subset U_q(\widehat{{{\mathfrak{g}}}})$ or ${{\mathfrak{g}}}\in Y({{\mathfrak{g}}})$, except in special cases, such as when ${{\mathfrak{g}}}\neq
A_r$. The idea is that $W_{{{\alpha}},k}(\zeta)$ is the “smallest” finite-dimensional ${{\mathfrak{g}}}[t]$-module, with largest component $V(k\omega_{{\alpha}})$ (the irreducible ${{\mathfrak{g}}}$-module), which deforms to a Yangian module.

KR-modules have been extensively studied in recent years, and much is known about their properties. In particular, their decomposition, and the decomposition of their tensor products, into 