The Bethe Equation at q = 0, The Möbius Inversion Formula,and Weight Multiplicities: III. The X |
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| Authors: | Kuniba Atsuo Nakanishi Tomoki Tsuboi Zengo |
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| Institution: | (1) Institute of Physics, University of Tokyo, Tokyo, 153-8902, Japan;(2) Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan;(3) Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan |
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| Abstract: | It 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 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. |
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| Keywords: | Bethe ansatz completeness Kirillov– Reshetikhin module Mö bius inversion formula Q-system quantum affine algebra string hypothesis weight multiplicity |
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