A refined Razumov-Stroganov conjecture
arXiv:cond-mat/0407477 · doi:10.1088/1742-5468/2004/08/P08009
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 prescribed last steps of all paths.
20 pages, 4 figures, uses epsf and harvmac macros a few typos corrected