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Higher Spin Generalization of the 6-Vertex Model and Macdonald Polynomials

Speaker: 
Tiago Dinis da Fonseca
Institution: 
Laboratoire d'Annecy-le-Vieux de Phisique Théorique, Université de Savoie, CNRS
Schedule: 
Wednesday, July 17, 2013 - 14:30 to 16:00
Location: 
A-136
Abstract: 

It is known that the 6-Vertex model is a quantum integrable  model, therefore we know, at least in theory, everything about it. For  example, in the case of Domain Wall Boundary Conditions, the partition  function is a relatively simple determinant (Izergin, 1987) and it is  related to a Schur polynomial. In a more recent work, Caradoc, Foda  and Kitanine (2006) tell us how to generalize this result for higher  spins. Based in their work, one can prove that the new partition  function is related to a Macdonald polynomial (dF and Balogh, to  appear). In this talk, I will describe the 6-vertex model, explain how  to create the higher spin model from the original model. And finally,  I will sketch how one can prove that this is indeed a Macdonald  polynomial.

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