BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Éric Vernier (LPSM\, CNRS et Sorbonne Université) DTSTART:20230123T100000Z DTEND:20230123T110000Z DTSTAMP:20260423T024516Z UID:IPHT-PHM/15 DESCRIPTION:Title: Onsager algebra and Ising-type structures in root-of-unity six-vertex mo dels\nby Éric Vernier (LPSM\, CNRS et Sorbonne Université) as part o f Séminaire de physique mathématique IPhT\n\nLecture held in Salle Claud e Itzykson\, Bât. 774\, Orme des Merisiers.\n\nAbstract\nI will start by reviewing a surprising connection between the six vertex model (or its hig her spin generalizations) and the Onsager algebra\, an infinite-dimensiona l Lie algebra which appeared in the solution of the two-dimensional Ising model. Using Kramers-Wannier duality\, a family of N-states integrable ver tex models/quantum spin chains are constructed having the Onsager algebra as a symmetry algebra. Those are then identified as the six-vertex model a nd its higher-spin descendents\, at specific "root-of-unity" values of the anisotropy parameter. While the integrability of six-vertex models is fam ously related to an underlying quantum group structure\, the enlarged Onsa ger symmetry could similarly be related to exotic quantum group representa tions occuring at root of unity. However\, this leaves certain aspects suc h as duality somewhat hidden in the six-vertex/quantum group formulation. I will therefore revert the logic and show that the (higher spin) root-of- unity six-vertex models can be re-expressed more simply in terms of Ising (clock) spins with products of 2-spins interactions only. The Onsager alge bra symmetry emerges naturally in this framework\, and the quantum-group r elated structures and Yang-Baxter equations of the vertex models can be tr aced back to simpler star-triangle equations in the spin formulation. This is based on E. Vernier\, E. O'Brien\, P. Fendley\, JSTAT (2019)\, and som e work in preparation.\n LOCATION:https://researchseminars.org/talk/IPHT-PHM/15/ END:VEVENT END:VCALENDAR