Bethe Equation at q=0, M\"obius Inversion Formula, and Weight Multiplicities: I. sl(2) case
Abstract
The Uq(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.
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