New symmetries of gl(N)-invariant Bethe vectors. (1st April 2019)

• Record Type: Journal Article
• Authors: Liashyk, A; Pakuliak, S Z; Ragoucy, E; Slavnov, N A
• Is Part Of: Journal of statistical mechanics. (2019:Apr.)
• Publication Date: 2019-04-01
• Subjects: 1; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab02f0
• Languages: English
• ISSNs: 1742-5468

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.