TY - JOUR

T1 - On the algebraic approach to solvable lattice models

AU - Belavin, Vladimir

AU - Gepner, Doron

N1 - Publisher Copyright:
© 2019, The Author(s).

PY - 2019/2/1

Y1 - 2019/2/1

N2 - We treat here interaction round the face (IRF) solvable lattice models. We study the algebraic structures underlining such models. For the three block case, we show that the Yang Baxter equation is obeyed, if and only if, the Birman-Murakami-Wenzl (BMW) algebra is obeyed. We prove this by an algebraic expansion of the Yang Baxter equation (YBE). For four blocks IRF models, we show that the BMW algebra is also obeyed, apart from the skein relation, which is different. This indicates that the BMW algebra is a sub-algebra for all models with three or more blocks. We find additional relations for the four block algebra using the expansion of the YBE. The four blocks result, that is the BMW algebra and the four blocks skein relation, is enough to define new knot invariant, which depends on three arbitrary parameters, important in knot theory.

AB - We treat here interaction round the face (IRF) solvable lattice models. We study the algebraic structures underlining such models. For the three block case, we show that the Yang Baxter equation is obeyed, if and only if, the Birman-Murakami-Wenzl (BMW) algebra is obeyed. We prove this by an algebraic expansion of the Yang Baxter equation (YBE). For four blocks IRF models, we show that the BMW algebra is also obeyed, apart from the skein relation, which is different. This indicates that the BMW algebra is a sub-algebra for all models with three or more blocks. We find additional relations for the four block algebra using the expansion of the YBE. The four blocks result, that is the BMW algebra and the four blocks skein relation, is enough to define new knot invariant, which depends on three arbitrary parameters, important in knot theory.

KW - Conformal Field Theory

KW - Integrable Field Theories

KW - Lattice Integrable Models

UR - http://www.scopus.com/inward/record.url?scp=85061216653&partnerID=8YFLogxK

U2 - 10.1007/JHEP02(2019)033

DO - 10.1007/JHEP02(2019)033

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AN - SCOPUS:85061216653

SN - 1126-6708

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 2

M1 - 33

ER -