A Proof of the KNS conjecture : Dr case
Abstract
We prove the Kuniba-Nakanishi-Suzuki (KNS) conjecture concerning the quantum dimension solution of the Q-system of type Dr obtained by a certain specialization of classical characters of the Kirillov-Reshetikhin modules. To this end, we use various symmetries of quantum dimensions. As a result, we obtain an explicit formula for the positive solution of the level k restricted Q-system of type Dr which plays an important role in dilogarithm identities for conformal field theories.
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