The quantum symmetric XXZ chain at Δ = -1/2, alternating-sign matrices and plane partitions

We consider the ground-state wavefunction of the quantum symmetric antiferromagnetic XXZ chain with open and twisted boundary conditions at Δ = -1/2, along with the ground-state wavefunction of the corresponding O(n) loop model at n = 1. Based on exact results for finite-size systems, sums involving the wavefunction components, and in some cases the largest component itself, are conjectured to be directly related to the total number of alternating-sign matrices and plane partitions in certain symmetry classes.