New Combinatorial Formulae for Nested Bethe Vectors

Abstract

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

v5: Formula and index errors in Sections 4-7 and Appendix A corrected