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Kuniba, Atsuo; Mangazeev, Vladimir V.; Maruyama, Shouya; Okado, Masato

doi:10.1016/j.nuclphysb.2016.09.016

Cited by 60 publications

(146 citation statements)

References 25 publications

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“…The main reason we do this is because (3.16) is now well defined even when I, J ∈ C. Although the 3D model projection outlined in this paper satisfies the Yang-Baxter equation for integral weights by construction, the equation (3.20) remains valid even for complex weights I, J, K ∈ C. The proof closely follows the arguments given in [26].…”

Section: The N-layer Projectionmentioning

confidence: 61%

“…We will establish a connection with the standard the U q ( sl n ) L-operator presented in [26] and also compare our results with some higher-spin examples of the U q ( sl 3 ) R-Matrix. We start with some remarks regarding the coefficient A (n) I,J (λ) in (3.17).…”

Section: Comparison With Other Resultsmentioning

confidence: 84%

“…Under the choice λ = q (J−I)/2 the U q ( sl 2 ) R-matrix of [19] reduces to the R-matrix of Povolotsky model [24] which satisfies stochasticity condition and defines a family of zero-range chipping models. A generalization of the Povolotsky model to arbitrary rank n − 1 was obtained in the recent paper [26].…”

Section: Reductions and Factorizationmentioning

confidence: 99%

“…In the recent paper [26] the above higher spin stochastic 6-vertex model has been generalized to the case of symmetric representations of the higher rank U q (A (1) n ) (or U q ( sl n+1 )). It was shown that even for a general n the corresponding R-matrix satisfies the sum rule required for a stochastic interpretation.…”

Section: Introductionmentioning

confidence: 99%

“…At a special point it gives a n species generalization of the Povolotsky model. However, most of the results in [26] were obtained using the machinery of quantum groups. Our strategy is to derive explicit formulas for the R-matrix related to symmetric representations of U q (A (1) n ) extending the method of [19].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Bosnjak¹,

Mangazeev²

2016

J. Phys. A: Math. Theor.

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In this paper we construct a new factorized representation of the R-matrix related to the affine algebra U q ( sl n ) for symmetric tensor representations with arbitrary weights. Using the 3D approach we obtain explicit formulas for the matrix elements of the R-matrix and give a simple proof that a "twisted" R-matrix is stochastic. We also discuss symmetries of the R-matrix, its degenerations and compare our formulas with other results available in the literature.

show abstract

Section: The N-layer Projectionmentioning

confidence: 61%

Section: Comparison With Other Resultsmentioning

confidence: 84%

Section: Reductions and Factorizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Bosnjak¹,

Mangazeev²

2016

J. Phys. A: Math. Theor.

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QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

Ferrando

Frassek

Казаков

2021

J. High Energ. Phys.

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We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the Dr Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric (fundamental) representations through r + 1 basic Q-functions. Our functional relations are consistent with the Q-operators proposed recently by one of the authors and verified explicitly on the level of operators at small finite length.

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Stochasticization of Solutions to the Yang–Baxter Equation

Borodin

Bufetov

2019

Ann. Henri Poincaré

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In this paper we introduce a procedure that, given a solution to the Yang-Baxter equation as input, produces a stochastic (or Markovian) solution to (a possibly dynamical version of) the Yang-Baxter equation. We then apply this "stochasticization procedure" to obtain three new, stochastic solutions to several different forms of the Yang-Baxter equation. The first is a stochastic, elliptic solution to the dynamical Yang-Baxter equation; the second is a stochastic, higher rank solution to the dynamical Yang-Baxter equation; and the third is a stochastic solution to a dynamical variant of the tetrahedron equation.

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Stochastic R matrix forUq(An(1))

Cited by 60 publications

References 25 publications

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

Stochasticization of Solutions to the Yang–Baxter Equation

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