Bethe Ansatz and the geography of rigged strings

Tadeusz Lulek. "Bethe Ansatz and the geography of rigged strings." Banach Center Publications 78.1 (2007): 231-247. <http://eudml.org/doc/282257>.

@article{TadeuszLulek2007,
abstract = {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.},
author = {Tadeusz Lulek},
journal = {Banach Center Publications},
keywords = {Robinson-Schensted algorithm; rigged strings; Bethe Ansatz; Weyl duality},
language = {eng},
number = {1},
pages = {231-247},
title = {Bethe Ansatz and the geography of rigged strings},
url = {http://eudml.org/doc/282257},
volume = {78},
year = {2007},
}

TY - JOUR
AU - Tadeusz Lulek
TI - Bethe Ansatz and the geography of rigged strings
JO - Banach Center Publications
PY - 2007
VL - 78
IS - 1
SP - 231
EP - 247
AB - 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.
LA - eng
KW - Robinson-Schensted algorithm; rigged strings; Bethe Ansatz; Weyl duality
UR - http://eudml.org/doc/282257
ER -