  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 prescribed last steps of all
paths.
