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Rigged configurations and the Bethe Ansatz

Anne Schilling
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Abstract

These notes arose from three lectures presented at the Summer School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter" held in Myczkowce, Poland, on September 11-18, 2002. We review rigged configurations and the Bethe Ansatz. In the first part, we focus on the algebraic Bethe Ansatz for the spin 1/2 XXX model and explain how rigged configurations label the solutions of the Bethe equations. This yields the bijection between rigged configurations and crystal paths/Young tableaux of Kerov, Kirillov and Reshetikhin. In the second part, we discuss a generalization of this bijection for the symmetry algebra $D_n^{(1)}$, based on work in collaboration with Okado and Shimozono.

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Anne Schilling. 2002-10-08. Rigged configurations and the Bethe Ansatz. https://doi.org/10.1142/9789812704474_0017

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