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Combinatorial formulae for nested Bethe vectors. (English) Zbl 1288.82024

Summary: We give combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for tensor products of irreducible evaluation modules over the Yangian \(Y({\mathfrak{gl}}_N)\) and the quantum affine algebra \(U_q(\widetilde{{\mathfrak{gl}}_N})\).

MSC:

82B23 Exactly solvable models; Bethe ansatz
17B80 Applications of Lie algebras and superalgebras to integrable systems
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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