qKZ equations and ground state of the O(1) loop model with open boundary conditions
Abstract
Description
We consider the qKZ equations based on the two boundaries Temperley Lieb algebra. We construct their solution in the case $s=q^{-3/2}$ using a recursion relation. At the combinatorial point $q^{1/2}= e^{-2πi/3}$ the solution reduces to the ground state of the dense O(1) loop model on a strip with open boundary conditions. We present an alternative construction of such ground state based on the knowledge of the ground state of the same model with mixed boundary conditions and prove that the sum rule as of its components is given by the product of four symplectic characters.
29 pages; 20 figures
29 pages; 20 figures