Abstract
We extend the Razumov–Stroganov conjecture relating the groundstate of the O(1) spin chain to alternating sign matrices by relating the groundstate of the monodromy matrix of the O(1) model to the so-called refined alternating sign matrices, i.e. with prescribed configuration of their first row, as well as to refined fully-packed loop configurations on a square grid, keeping track both of the loop connectivity and of the configuration of their top row. We also conjecture a direct relation between this groundstate and refined totally symmetric self-complementary plane partitions, namely, in their formulation as sets of non-intersecting lattice paths, with the prescribed last steps of all paths.