SOS model partition function and the elliptic weight functions

Abstract

We generalize a recent observation [arXiv:math/0610433] that the partition function of the 6-vertex model with domain-wall boundary conditions can be obtained by computing the projections of the product of the total currents in the quantum affine algebra $U_q({\widehat{\mathfrak{sl}}}_2)$ in its current realization. A generalization is proved for the the elliptic current algebra [arXiv:q-alg/9703018,arXiv:q-alg/9601022]. The projections of the product of total currents are calculated explicitly and are represented as integral transforms of the product of the total currents. We prove that the kernel of this transform is proportional to the partition function of the SOS model with domain-wall boundary conditions.

21 pages, 5 figures, requires iopart package

References in corpus (6)

• Elliptic quantum groups $E_{\tau ,\eta }(s{l}_2)$ and quasi-Hopf algebras
• Off-shell Bethe vectors and Drinfeld currents
• Separation of variables for quantum integrable systems on elliptic curves
• Weight function for the quantum affine algebra $U_q({\widehat{sl}}_3)$
• Factorization of the Universal R-matrix for $U_q({\widehat{sl}}_2)$
• Classical elliptic current algebras

Cited by in corpus (35)

• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• Antiperiodic dynamical 6-vertex model by separation of variables II: Functional equations and form factors
• Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
• Multiple integral representation for the trigonometric SOS model with domain wall boundaries
• Refined functional relations for the elliptic SOS model
• Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
• The 8-vertex model with quasi-periodic boundary conditions
• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• Partition function of the eight-vertex model with domain wall boundary condition
• Scalar products of Bethe vectors in the 8-vertex model
• Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model
• Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end
• Partition function of the trigonometric SOS model with reflecting end
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Integral formula for elliptic SOS models with domain walls and a reflecting end
• Functional relations and the Yang-Baxter algebra
• Multi-point local height probabilities of the CSOS model within the algebraic Bethe Ansatz framework
• Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice
• Elliptic pfaffians and solvable lattice models
• The Functional Method for the Domain-Wall Partition Function
• Elliptic supersymmetric integrable model and multivariable elliptic functions
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• On the elliptic ${\mathfrak{gl}}_2$ solid-on-solid model: functional relations and determinants
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula
• Action of the monodromy matrix entries in the generalized algebraic Bethe ansatz
• New determinants in the 8VSOS model with domain-wall boundaries
• Higher rank elliptic partition functions and multisymmetric elliptic functions
• Felder's elliptic quantum group and elliptic hypergeometric series on the root system A_n
• A duality formula between elliptic determinants
• Integrable models and $K$-theoretic pushforward of Grothendieck classes
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint
• Modified rational six vertex model on a rectangular lattice : new formula, homogeneous and thermodynamic limits
• Elliptic free-fermion model with OS boundary and elliptic Pfaffians