$B_k$ Spin Vertex Models and Quantum Algebras

Doron Gepner

doi:10.1016/j.nuclphysb.2020.115116

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arXiv · 2005.02708

$B_k$ Spin Vertex Models and Quantum Algebras

Doron Gepner

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Abstract

We construct new solvable vertex models based on the spin representation of the Lie algebra $B_k$. We use these models to study the algebraic structure underlying such vertex theories. We show that all the $B_k$ 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.

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Doron Gepner. 2020-05-06. $B_k$ Spin Vertex Models and Quantum Algebras. https://doi.org/10.1016/j.nuclphysb.2020.115116

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