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arXiv:1810.00364 · Journal of Statistical Mechanics Theory and Experiment

New symmetries of g l ( N ) -invariant Bethe vectors

Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak, E. Ragoucy, N A Slavnov

Published Apr 1, 2019• 15 citations

Abstract

Abstract We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing -invariant R -matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix. The second type is associated to a monodromy matrix closely related to the inverse of the monodromy matrix. We show that these two types of Bethe vectors are identical up to normalization and reshuffling of the Bethe parameters. To prove this correspondence we use the current approach. This identity gives new combinatorial relations for the scalar products of the Bethe vectors. The q -deformed case, as well as the superalgebra case, are also evoked in the conclusion.

DOI: 10.1088/1742-5468/ab02f0

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Scalar products of Bethe vectors in models with

\mathfrak{gl}(2|1)

symmetry 1. Super-analog of Reshetikhin formula

We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing

\mathfrak{gl}(2|1)

symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with

\mathfrak{gl}(1|1)

symmetry.