2024/12/06 by Liashyk, Andrii, Pakuliak, Stanislav, Ragoucy, Eric
#17B80 #82B23 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2412.05224
A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type \mathfrakgln or type \mathfrako2n+1 symmetries. These recurrence relations describe how to add a single parameter z 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 z. 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.