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Explore the intricate connections between duality, Onsager algebra, and Ising-type structures in root-of-unity six-vertex models in this 47-minute conference talk by Eric Vernier at the Centre de recherches mathématiques (CRM). Delve into the existence of new structures in the six-vertex model and its higher spin generalizations at special anisotropy values. Discover the surprising link between the Onsager algebra, first appearing in Onsager's solution of the two-dimensional Ising model, and the six-vertex model. Learn how Kramers-Wannier duality led to the construction of N-states integrable vertex models with Onsager algebra symmetry. Investigate the relationship between enlarged Onsager symmetry and exotic quantum group representations at root of unity. Examine how root-of-unity six-vertex models can be re-expressed in terms of Ising spins with simpler interactions, revealing the natural emergence of Onsager algebra symmetry and tracing quantum-group related structures back to star-triangle equations in the spin formulation.
