Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.03381 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908865917878272 |
|---|---|
| author | Lu, Ming Pan, Xiaolong |
| author_facet | Lu, Ming Pan, Xiaolong |
| contents | Qin established the geometric realization of entire quantum groups via perverse sheaves, which further give rise to dual canonical bases with integral and positive structure constants for quantum groups of type ADE. In this paper, we prove that the dual canonical bases of (Drinfeld double) quantum groups coincide with Berenstein--Greenstein's double canonical bases, by reinterpreting their intricate algebraic construction via the geometry of NKS quiver varieties. This result settles several conjectures therein, including those on positivity and invariance under braid group actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03381 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dual and double canonical bases of quantum groups Lu, Ming Pan, Xiaolong Quantum Algebra Representation Theory Qin established the geometric realization of entire quantum groups via perverse sheaves, which further give rise to dual canonical bases with integral and positive structure constants for quantum groups of type ADE. In this paper, we prove that the dual canonical bases of (Drinfeld double) quantum groups coincide with Berenstein--Greenstein's double canonical bases, by reinterpreting their intricate algebraic construction via the geometry of NKS quiver varieties. This result settles several conjectures therein, including those on positivity and invariance under braid group actions. |
| title | Dual and double canonical bases of quantum groups |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2603.03381 |