$\ell$-restricted $Q$-systems and quantum affine algebras
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 o...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2014-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2375/pdf |
| _version_ | 1797270312120745984 |
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| author | Anne-Sophie Gleitz |
| author_facet | Anne-Sophie Gleitz |
| author_sort | Anne-Sophie Gleitz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:02:16Z |
| format | Article |
| id | doaj.art-d30addde25034905a5ad607b0662e0b4 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:16Z |
| publishDate | 2014-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-d30addde25034905a5ad607b0662e0b42024-03-07T14:53:19ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502014-01-01DMTCS Proceedings vol. AT,...Proceedings10.46298/dmtcs.23752375$\ell$-restricted $Q$-systems and quantum affine algebrasAnne-Sophie Gleitz0https://orcid.org/0000-0002-1212-4962Laboratoire de Mathématiques Nicolas OresmeKuniba, 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.https://dmtcs.episciences.org/2375/pdfkirillov-reshetikhin modulesrepresentation theorycharactersq-systemsquantum dimensionkuniba nakanishi suzuki (kns)[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Anne-Sophie Gleitz $\ell$-restricted $Q$-systems and quantum affine algebras Discrete Mathematics & Theoretical Computer Science 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] |
| title | $\ell$-restricted $Q$-systems and quantum affine algebras |
| title_full | $\ell$-restricted $Q$-systems and quantum affine algebras |
| title_fullStr | $\ell$-restricted $Q$-systems and quantum affine algebras |
| title_full_unstemmed | $\ell$-restricted $Q$-systems and quantum affine algebras |
| title_short | $\ell$-restricted $Q$-systems and quantum affine algebras |
| title_sort | ell restricted q systems and quantum affine algebras |
| topic | 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] |
| url | https://dmtcs.episciences.org/2375/pdf |
| work_keys_str_mv | AT annesophiegleitz ellrestrictedqsystemsandquantumaffinealgebras |