Bk spin vertex models and quantum algebras

Doron Gepner

doi:https://doi.org/10.1016/j.nuclphysb.2020.115116

Bk spin vertex models and quantum algebras

Doron Gepner

Department of Particle Physics and Astrophysics

Weizmann Institute of Science

Research output: Contribution to journal › Article

Abstract

We construct new solvable vertex models based on the spin representation of the Lie algebra Bk. We use these models to study the algebraic structure underlying such vertex theories. We show that all the Bk spin vertex models obey a version of the BMW algebra along with extra relations that are called n–CB (conformal braiding) algebras. These algebras were discussed before for various IRF (interaction round the face) models. Here we establish that the same algebras hold for vertex models.

Original language	English
Article number	115116
Number of pages	11
Journal	Nuclear Physics B
Volume	958
Early online date	21 Jul 2020
DOIs	https://doi.org/10.1016/j.nuclphysb.2020.115116
State	Published - Sep 2020

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title = "Bk spin vertex models and quantum algebras",

abstract = "We construct new solvable vertex models based on the spin representation of the Lie algebra Bk. We use these models to study the algebraic structure underlying such vertex theories. We show that all the Bk spin vertex models obey a version of the BMW algebra along with extra relations that are called n–CB (conformal braiding) algebras. These algebras were discussed before for various IRF (interaction round the face) models. Here we establish that the same algebras hold for vertex models.",

author = "Doron Gepner",

note = "It is my pleasure to thank Hans Wenzl for many discussions, encouragement and for sending me his paper [20]. I am also grateful to Ida Deichaite for remarks on the manuscript and valuable impetus. I also thank Jian-Rong Li for comments. I thank Vladimir Belavin for help with the calculations.",

year = "2020",

month = sep,

doi = "https://doi.org/10.1016/j.nuclphysb.2020.115116",

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AU - Gepner, Doron

N1 - It is my pleasure to thank Hans Wenzl for many discussions, encouragement and for sending me his paper [20]. I am also grateful to Ida Deichaite for remarks on the manuscript and valuable impetus. I also thank Jian-Rong Li for comments. I thank Vladimir Belavin for help with the calculations.

PY - 2020/9

Y1 - 2020/9

N2 - We construct new solvable vertex models based on the spin representation of the Lie algebra Bk. We use these models to study the algebraic structure underlying such vertex theories. We show that all the Bk spin vertex models obey a version of the BMW algebra along with extra relations that are called n–CB (conformal braiding) algebras. These algebras were discussed before for various IRF (interaction round the face) models. Here we establish that the same algebras hold for vertex models.

AB - We construct new solvable vertex models based on the spin representation of the Lie algebra Bk. We use these models to study the algebraic structure underlying such vertex theories. We show that all the Bk spin vertex models obey a version of the BMW algebra along with extra relations that are called n–CB (conformal braiding) algebras. These algebras were discussed before for various IRF (interaction round the face) models. Here we establish that the same algebras hold for vertex models.

U2 - https://doi.org/10.1016/j.nuclphysb.2020.115116

DO - https://doi.org/10.1016/j.nuclphysb.2020.115116

M3 - مقالة

SN - 0550-3213

VL - 958

JO - Nuclear Physics B

JF - Nuclear Physics B

M1 - 115116

ER -

Bk spin vertex models and quantum algebras

Abstract

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