Combinatorial Formulae for Nested Bethe Vectors

Abstract

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 $U_q(\widetilde{{\mathfrak{gl}}_N})$. The results of the paper were obtained in 1998 and were used in math.QA/9905137, math.QA/0302148, math.QA/0610517.

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Cited by in corpus (31)

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• Bethe vectors of GL(3)-invariant integrable models
• Highest coefficient of scalar products in SU(3)-invariant integrable models
• Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Scalar products in generalized models with SU(3)-symmetry
• Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety
• On Bethe vectors in ${\mathfrak{gl}}_3$-invariant integrable models
• Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric $R$-Matrix
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Bethe Ansatz for the Universal Weight Function
• Bethe Ansatz and Bethe Vectors Scalar Products
• A computation of an universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)
• Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel
• Weight function for the quantum affine algebra $U_q({\widehat{sl}}_3)$
• Multiple commutation relations in the models with gl(2|1) symmetry
• Introduction to the nested algebraic Bethe ansatz
• Nested algebraic Bethe ansatz for deformed orthogonal and symplectic spin chains
• Bethe vectors for orthogonal integrable models
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors
• Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions
• Elliptic and K-theoretic stable envelopes and Newton polytopes
• On the universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)
• Partial flag varieties, stable envelopes and weight functions
• Bow varieties---geometry, combinatorics, characteristic classes
• Landau-Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• Generating Series for Nested Bethe Vectors
• Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
• Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis