We demonstrate the way in which composition of two famous combinatorial bijections, of Robinson-Schensted and Kerov-Kirillov-Reshetikhin, applied to the Heisenberg model of magnetic ring with spin 1/2, defines the geography of rigged strings (which label exact eigenfunctions of the Bethe Ansatz) on the classical configuration space (the set of all positions of the system of r reversed spins). We point out that each l-string originates, in the language of this bijection, from an island of l consecutive reversed spins. We also explain travel of l-strings along orbits of the translation group of the ring.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-17,
author = {Tadeusz Lulek},
title = {Bethe Ansatz and the geography of rigged strings},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {231-247},
zbl = {1147.82012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-17}
}
Tadeusz Lulek. Bethe Ansatz and the geography of rigged strings. Banach Center Publications, Tome 75 (2007) pp. 231-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-17/