Skip to content

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

P. Zinn-Justin

math-pharXiv:math-ph/0610067

Abstract

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.

Create a lesson