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 -