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Discrete Mathematics & Theoretical Computer Science |
Kuniba, Nakanishi, and Suzuki (1994) have formulated a general conjecture expressing the positive solution of an $\ell$-restricted $Q$-system in terms of quantum dimensions of Kirillov-Reshetikhin modules. After presenting this conjecture, we sketch a proof for the exceptional type $E_6$ following our preprint (2013). In types $E_7$ and $E_8$, we prove positivity for a subset of the nodes of the Dynkin diagram, and we reduce the positivity for the remaining nodes to the conjectural iterated log-concavity of certain explicit sequences of real algebraic numbers.
Source : ScholeXplorer
IsRelatedTo ARXIV 1010.1344 Source : ScholeXplorer IsRelatedTo DOI 10.1088/1751-8113/44/10/103001 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1010.1344
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