A refined Razumov-Stroganov conjecture
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.
Cite
@article{arxiv.cond-mat/0407477,
title = {A refined Razumov-Stroganov conjecture},
author = {P. Di Francesco},
journal= {arXiv preprint arXiv:cond-mat/0407477},
year = {2009}
}
Comments
20 pages, 4 figures, uses epsf and harvmac macros a few typos corrected