The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61488It is shown that the numbers of off-diagonal solutions to the U_q(X^{(r)}_N) Bethe equation at q=0 coincide with the coefficients in the recently introduced canonical power series solution of the Q-system. Conjecturally the canonical solutions are characters of the KR (Kirillov-Reshetikhin) modules. This implies that the numbers of off-diagonal solutions agree with the weight multiplicities, which is interpreted as a formal completeness of the U_q(X^{(r)}_N) Bethe ansatz at q=0.11 pages, LaTeX2e, no figureQuantum AlgebraHigh Energy Physics - TheoryExactly Solvable and Integrable Systems81R10 (Primary), 82B23 (Secondary)The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N casetext