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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.00524 |
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| _version_ | 1866911350635102208 |
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| author | Chen, Jiayi Lu, Ming Pan, Xiaolong Ruan, Shiquan Wang, Weiqiang |
| author_facet | Chen, Jiayi Lu, Ming Pan, Xiaolong Ruan, Shiquan Wang, Weiqiang |
| contents | Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of arbitrary finite type, which are further shown to be preserved by the ibraid group action; this recovers the results of Lu-Pan in ADE type obtained earlier in a geometric approach. Moreover, we identify the dual canonical basis for the Drinfeld double quantum group of arbitrary finite type, which is realized via iHopf algebra on the double Borel, with Berenstein-Greenstein's double canonical basis, settling several of their conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00524 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | iQuantum groups and iHopf algebras II: dual canonical bases Chen, Jiayi Lu, Ming Pan, Xiaolong Ruan, Shiquan Wang, Weiqiang Quantum Algebra Representation Theory Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of arbitrary finite type, which are further shown to be preserved by the ibraid group action; this recovers the results of Lu-Pan in ADE type obtained earlier in a geometric approach. Moreover, we identify the dual canonical basis for the Drinfeld double quantum group of arbitrary finite type, which is realized via iHopf algebra on the double Borel, with Berenstein-Greenstein's double canonical basis, settling several of their conjectures. |
| title | iQuantum groups and iHopf algebras II: dual canonical bases |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2601.00524 |