Rectangular Recurrence Relations in $\mathfrak{gl}_{n}$ and $\mathfrak{o}_{2n+1}$ Invariant Integrable Models
Quantum Algebra
2025-09-23 v3 Exactly Solvable and Integrable Systems
Abstract
A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type or type symmetries. These recurrence relations describe how to add a single parameter to specific subsets of Bethe parameters, expressing the resulting Bethe vector as a linear combination of monodromy matrix entries that act on Bethe vectors which do not depend on . We refer to these recurrence relations as rectangular because the monodromy matrix entries involved are drawn from the upper-right rectangular part of the matrix. This construction is achieved within the framework of the zero mode method.
Cite
@article{arxiv.2412.05224,
title = {Rectangular Recurrence Relations in $\mathfrak{gl}_{n}$ and $\mathfrak{o}_{2n+1}$ Invariant Integrable Models},
author = {Andrii Liashyk and Stanislav Pakuliak and Eric Ragoucy},
journal= {arXiv preprint arXiv:2412.05224},
year = {2025}
}