Physics – Mathematical Physics
Scientific paper
2006-02-13
J. Phys. A: Math. Gen. 39 (2006) 9015-9033
Physics
Mathematical Physics
Talk presented by F.C. at the Short Program of the Centre de Recherches Mathematiques: Random Matrices, Random Processes and I
Scientific paper
10.1088/0305-4470/39/28/S15
The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific values of the parameters of the model, corresponding to 1-, 2- and 3-enumerations of Alternating Sign Matrices (ASMs), these polynomials specialize to classical ones (Continuous Hahn, Meixner-Pollaczek, and Continuous Dual Hahn, respectively). As a consequence, a unified and simplified treatment of ASMs enumerations turns out to be possible, leading also to some new results such as the refined 3-enumerations of ASMs. Furthermore, the use of orthogonal polynomials allows us to express, for generic values of the parameters of the model, the partition function of the (partially) inhomogeneous model in terms of the one-point boundary correlation functions of the homogeneous one.
Colomo Filippo
Pronko A. G.
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