New Combinatorial Formulae for Nested Bethe Vectors

We give new combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for the evaluation modules over the Yangian $Y({\mathfrak{g}\mathfrak{l}}_4)$. The case of $Y({\mathfrak{g}\mathfrak{l}}_n)$ for an arbitrary $n$ is considered in [Lett. Math. Phys. 115 (2025), 12, 20 pages, arXiv:2402.15717].