Schoutens's conjecture on the Yangian structure of an affine level-1 module

Let ${\cal L}(\Lambda_k)$ be the level $1$ integrable module of $\widehat{sl}_n$, and let the character decomposition in equation (26a) be the decomposition obtained from the irreducible $Y(sl_n)$-characters associated with the spectral degeneracies. Schoutens's conjecture. The decomposition describes the $Y(sl_n)$-module structure on ${\cal L}(\Lambda_k)$ considered by Schoutens. The paper proves the relevant irreducible Yangian characters and notes agreement with the partially studied module structure, while the asserted full module-structure identification remains conjectural.