Geometry and Integrability in Mathematical Physics GIMP'06
May 15 - 19, 2006, Moscow, Russia
Philippe Di Francesco
SPhT CEA Saclay, France
Physics and combinatorics: the miracles of integrability
We discuss the integrable structure underlying integer sequences such as the numbers of nxn alternating sign matrices and the degrees of nilpotent upper triangular nxn matrix varieties. We obtain a proof of the Razumov-Stroganov sum rule for inhomogeneous loop models, as well as a proof of a generalized Razumov-Stroganov conjecture relating minimal polynomial solutions of the Quantum Khniknik-Zamolodchikov equation at $q=-1$ to multidegrees of the components of nilpotent upper triangular matrix varieties.
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