## Gleitz, Anne-Sophie - $\ell$-restricted $Q$-systems and quantum affine algebras

dmtcs:2375 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
$\ell$-restricted $Q$-systems and quantum affine algebras

Authors: Gleitz, Anne-Sophie

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 : oai:HAL:hal-01207615v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: Kirillov-Reshetikhin modules,representation theory,characters,Q-systems,quantum dimension,Kuniba Nakanishi Suzuki (KNS),[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]