Bethe Equation at q=0, Möbius Inversion Formula, and Weight Multiplicities: I. sl(2) case

1999/09/30 by Atsuo Kuniba, Tomoki Nakanishi
Mathematics · Physics and Astronomy · #math.QA #cond-mat.stat-mech #nlin.SI #solv-int #msc:81R10

paper · pdf

published as Prog. Math. Phys. 191 "Physical Combinatorics" (2000) 185--216 · latex2e, 35pages, no figure

arxiv created 1999/11/19 · arxiv updated 2009/11/30

Abstract

The U_q(sl(2)) Bethe equation is studied at q=0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and coincides with the weight multiplicities of the quantum space.

Related

• The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^(r)_N case
• Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems
• Completing Bethe's equations at roots of unity
• On the new form of Bethe ansatz equations and separation of variables in the sl₃ Gaudin model
• Bethe ansatz equations for quantum N=2 KdV systems