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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2007

Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices

Résumé

The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley--Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its minimal degree solution described. As a result, the sum of the properly normalized components of the ground state in size L is computed and shown to be equal to the number of Horizontally and Vertically Symmetric Alternating Sign Matrices of size 2L+3. A refined counting is also considered.

Dates et versions

hal-00129350 , version 1 (06-02-2007)

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Paul Zinn-Justin. Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices. Journal of Statistical Mechanics: Theory and Experiment, 2007, pp.P01007. ⟨hal-00129350⟩
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