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Quantum affine symmetry in vertex models

Makoto Idzumi·Kenji Iohara·Michio Jimbo·Tetsuji Miwa·Toshiki Nakashima·Tetsuji Tokihiro
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Abstract

We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin $1/2$, and that the $n$-particle space has an RSOS-type structure rather than a simple tensor product of the $1$-particle space. This agrees with the picture proposed earlier by Reshetikhin.

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Makoto Idzumi, Kenji Iohara, Michio Jimbo, Tetsuji Miwa, Toshiki Nakashima, Tetsuji Tokihiro. 1992-08-27. Quantum affine symmetry in vertex models. https://doi.org/10.1142/s0217751x9300062x

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