Weighted Razumov-Stroganov correspondences

Luigi Cantini (LPTM Universite de Cergy Pontoise)

Tuesday 11th November, 2014 15:00-16:00 Maths 203


In 2001 Razumov and Stroganov conjectured that the (properly normalized) stationary probabilities of the periodic Temperley-Lieb Stochastic model enumerate fully-packed loop (FPL) configurations on the square, with alternating boundary conditions, refined according to the link pattern for the boundary points. The correspondence between these apparently unrelated subjects and their rich combinatorial content have arisen a lot of interest both in the physics and in the mathematics community. In this talk we present the subject with a focus on the implications of the integrable structure of the loop model on the Enumerative Combinatorics of FPL and other combinatorial objects such as Alternating Sign Matrices. We shall also present generalizations of the Razumov-Stroganov correspondence obtained by introducing boundary weights on the FPLs. 

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