An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras
Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the analogous conjecture is true. Our result applies to the d...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211097 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras. Fan Qin. SIGMA 16 (2020), 122, 22 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725257223208960 |
|---|---|
| author | Qin, Fan |
| author_facet | Qin, Fan |
| citation_txt | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras. Fan Qin. SIGMA 16 (2020), 122, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the analogous conjecture is true. Our result applies to the dual canonical bases of quantum unipotent subgroups. It also applies to the -analogs of -characters of simple modules of quantum affine algebras.
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| first_indexed | 2026-03-21T08:02:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211097 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T08:02:40Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Qin, Fan 2025-12-23T13:14:19Z 2020 An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras. Fan Qin. SIGMA 16 (2020), 122, 22 pages 1815-0659 2020 Mathematics Subject Classification: 13F60 arXiv:2004.12466 https://nasplib.isofts.kiev.ua/handle/123456789/211097 DOI: https://doi.org/10.3842/SIGMA.2020.122 Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the analogous conjecture is true. Our result applies to the dual canonical bases of quantum unipotent subgroups. It also applies to the -analogs of -characters of simple modules of quantum affine algebras. The author thanks the referees for their helpful suggestions. He also thanks an anonymous referee for informing him of the work [21]. The author was supported by the National Natural Science Foundation of China (Grant No. 11701365). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras Article published earlier |
| spellingShingle | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras Qin, Fan |
| title | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras |
| title_full | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras |
| title_fullStr | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras |
| title_full_unstemmed | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras |
| title_short | An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras |
| title_sort | analog of leclerc's conjecture for bases of quantum cluster algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211097 |
| work_keys_str_mv | AT qinfan ananalogofleclercsconjectureforbasesofquantumclusteralgebras AT qinfan analogofleclercsconjectureforbasesofquantumclusteralgebras |