Bethe vectors for orthogonal integrable models. (English. Russian original) Zbl 1441.81106
Theor. Math. Phys. 201, No. 2, 1545-1564 (2019); translation from Teor. Mat. Fiz. 201, No. 2, 153-174 (2019).
Summary: We consider quantum integrable models associated with the \(\mathfrak{so}_3\) algebra and describe Bethe vectors of these models in terms of the current generators of the \(\mathcal{D}Y(\mathfrak{so}_3)\) algebra. To implement this program, we use an isomorphism between the \(R\)-matrix and the Drinfeld current realizations of the Yangians and their doubles for classical type \(B\)-, \(C\)-, and \(D\)-series algebras. Using these results, we derive the actions of the monodromy matrix elements on off-shell Bethe vectors. We obtain recurrence relations for off-shell Bethe vectors and Bethe equations for on-shell Bethe vectors. The formulas for the action of the monodromy matrix elements can also be used to calculate scalar products in the models associated with the \(\mathfrak{so}_3\) algebra.
MSC:
| 81Q80 | Special quantum systems, such as solvable systems |
| 81Q40 | Bethe-Salpeter and other integral equations arising in quantum theory |
| 16T25 | Yang-Baxter equations |
| 82B23 | Exactly solvable models; Bethe ansatz |
| 82C23 | Exactly solvable dynamic models in time-dependent statistical mechanics |
| 17B20 | Simple, semisimple, reductive (super)algebras |
| 17B45 | Lie algebras of linear algebraic groups |
| 14D05 | Structure of families (Picard-Lefschetz, monodromy, etc.) |
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