New Elliptic Solutions of the Yang–Baxter Equation

Chicherin, Dmitry; Derkachov, S. E.; Spiridonov, V. P.

doi:10.1007/s00220-016-2590-2

Cited by 14 publications

(23 citation statements)

References 63 publications

(353 reference statements)

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“…(4.6) 6 In connection with surface defects, it should also be noted that the transfer matrices in the symmetric powers of the vector representation are residues of a certain integral operator [29,57]. In [58], the general fused L-operator were obtained for the elliptic modular double for N = 2 via reduction of the BSDS R-operator.…”

Section: Fusion Procedures and Exterior Powers Of The Vector Representmentioning

confidence: 99%

Surface defects and elliptic quantum groups

Yagi

2017

J. High Energ. Phys.

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A brane construction of an integrable lattice model is proposed. The model is composed of Belavin's R-matrix, Felder's dynamical R-matrix, the Bazhanov-SergeevDerkachov-Spiridonov R-operator and some intertwining operators. This construction implies that a family of surface defects act on supersymmetric indices of four-dimensional N = 1 supersymmetric field theories as transfer matrices related to elliptic quantum groups.

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Section: Fusion Procedures and Exterior Powers Of The Vector Representmentioning

confidence: 99%

Surface defects and elliptic quantum groups

Yagi

2017

J. High Energ. Phys.

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“…with periodic boundary conditions that σ L+1 = σ 1 andσ L+1 =σ 1 one can prove that T qTr = T rTq . If one has such a family of commuting transfer matrices then a partition those solution and refer to the original papers [26,27,[43][44][45][46]. 7 Note that in the literature "the star-triangle relation" often is used also for the IRF-type models, see, e.g.…”

Section: Integrability Of Models: Star-triangle Relationmentioning

confidence: 99%

Integrable Lattice Spin Models from Supersymmetric Dualities

Gahramanov

Jafarzade

2018

Phys. Part. Nuclei Lett.

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Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the quiver diagram, the partition function of the lattice model is the partition function of the gauge theory and the Yang-Baxter equation expresses the identity of partition functions for dual pairs. This correspondence is a powerful tool which enables us to generate new integrable models. The aim of the present paper is to give a short account on a progress in integrable lattice models which has been made due to the relationship with supersymmetric gauge theories.MSC classes: 81T60, 16T25, 14K25, 33D60, 33E20, 33D90, 39A13

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“…In [9] the integral R-operator for the elliptic double has been taken as a starting point and restrictions of this operator to finite-dimensional representations have been implemented. In particular, the restriction to a (n + 1)-dimensional representation in the first space at spin g n ≡ (n + 1)η + τ 2 , n ∈ Z ≥0 , has been considered.…”

Section: Sklyanin Algebra and Elliptic Factorizationmentioning

confidence: 99%

“…In the accompanying paper [9] the analogous restriction of the general R-operator [13] has been carried out for elliptic deformations of sℓ 2 , which are the Sklyanin algebra and the elliptic modular double [38].…”

Section: Introductionmentioning

confidence: 99%

Matrix Factorization for Solutions of the Yang–Baxter Equation

Derkachov

Chicherin

2016

J Math Sci

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We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finitedimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sℓ 2 , the modular double (trigonometric deformation) and the Sklyanin algebra (elliptic deformation). The solutions are matrices with operator entries. The matrix elements are differential operators in the case of sℓ 2 , finite-difference operators with trigonometric coefficients in the case of the modular double, or finite-difference operators with coefficients constructed out of Jacobi theta functions in the case of the Sklyanin algebra. We find a new factorized form of the rational, trigonometric, and elliptic solutions, which drastically simplifies them. We show that they are products of several simply organized matrices and obtain for them explicit formulae.

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New Elliptic Solutions of the Yang–Baxter Equation

Cited by 14 publications

References 63 publications

Surface defects and elliptic quantum groups

Surface defects and elliptic quantum groups

Integrable Lattice Spin Models from Supersymmetric Dualities

Matrix Factorization for Solutions of the Yang–Baxter Equation

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