Bethe Ansatz and the geography of rigged strings

Volume 78 / 2007

Tadeusz Lulek Banach Center Publications 78 (2007), 231-247 MSC: Primary 20C30; Secondary 70G10. DOI: 10.4064/bc78-0-17


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.


  • Tadeusz LulekRzeszów University of Technology
    Powstańców Warszawy 6
    35-959 Rzeszów, Poland

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