TY - JOUR

T1 - The 5-CB algebra and fused SU(2) lattice models

AU - Belavin, Vladimir

AU - Gepner, Doron

N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd.

PY - 2021/9

Y1 - 2021/9

N2 - We study the fused SU(2) models put forward by Date et al, that are a series of models with arbitrary number of blocks, which is the degree of the polynomial equation obeyed by the Boltzmann weights. We demonstrate by a direct calculation that a version of Birman-Murakami-Wenzl (BMW) algebra [1, 2] is obeyed by five, six and seven blocks models, conjecturing that the BMW algebra is a part of the algebra valid for any model with more than two blocks. To establish this conjecture, we assume that a certain ansatz holds for the baxterization of the models. We use the Yang-Baxter equation to describe explicitly the algebra for five blocks, obtaining 19 additional non-trivial relations. We name this algebra 5-CB (conformal braiding) algebra. Our method can be utilized to describe the algebra for any solvable model of this type and for any number of blocks.

AB - We study the fused SU(2) models put forward by Date et al, that are a series of models with arbitrary number of blocks, which is the degree of the polynomial equation obeyed by the Boltzmann weights. We demonstrate by a direct calculation that a version of Birman-Murakami-Wenzl (BMW) algebra [1, 2] is obeyed by five, six and seven blocks models, conjecturing that the BMW algebra is a part of the algebra valid for any model with more than two blocks. To establish this conjecture, we assume that a certain ansatz holds for the baxterization of the models. We use the Yang-Baxter equation to describe explicitly the algebra for five blocks, obtaining 19 additional non-trivial relations. We name this algebra 5-CB (conformal braiding) algebra. Our method can be utilized to describe the algebra for any solvable model of this type and for any number of blocks.

KW - conformal field theory

KW - quantum algebras

KW - solvable lattice models

UR - http://www.scopus.com/inward/record.url?scp=85114648527&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/abe77b

DO - 10.1088/1751-8121/abe77b

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AN - SCOPUS:85114648527

SN - 1751-8113

VL - 54

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 37

M1 - 375202

ER -