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arXiv:math-ph/0411034

Solving Baxter's TQ-equation via representation theory

Christian Korff

Published Nov 9, 2004• 7 citations
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Abstract

Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is given depending on a new free parameter. Specializing this general construction to even roots of unity and lattices with an odd number of columns two linearly independent operator solutions of Baxter's TQ equation are obtained as special limits.

DOI
10.48550/arxiv.math-ph/0411034

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Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is given depending on a new free parameter. Specializing this general construction to even roots of unity and lattices with an odd number of columns two linearly independent operator solutions of Baxter's TQ equation are obtained as special limits.
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At roots of unity the NNN-state integrable chiral Potts model and the six-vertex model descend from each other with the τ2τ_2τ2​ model as the intermediate. We shall discuss how different gauge choices in the six-vertex model lead to two different quantum group constructions with different qqq-Pochhammer symbols, one construction only working well for NNN odd, the other equally well for all NNN. We also address the generalization based on the sl(m,n)(m,n)(m,n) vertex model.