Calabi-Yau techniques for Namikawa-Weyl groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916552771633152 |
|---|---|
| author | van de Kreeke, Jasper |
| author_facet | van de Kreeke, Jasper |
| contents | The field of symplectic singularities aims to build a 21st century Lie theory. A key development is the Namikawa-Weyl group, which generalizes the classical Weyl group of Lie algebras. Another cornerstone is the integration of categorical Calabi-Yau techniques, capturing the rich algebraic structure of these singularities. In this paper, we develop a systematic strategy to determine Namikawa-Weyl groups for representation spaces of Calabi-Yau-2 algebras, leveraging local-to-global functors, symmetry analysis, and $ A_{\infty} $-methods. Applying this approach to quiver varieties, we carry out the detailed calculations and recover Yaochen Wu's result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calabi-Yau techniques for Namikawa-Weyl groups van de Kreeke, Jasper Representation Theory Algebraic Geometry Symplectic Geometry 16G20 (Primary) 14J42, 53D30 (Secondary) The field of symplectic singularities aims to build a 21st century Lie theory. A key development is the Namikawa-Weyl group, which generalizes the classical Weyl group of Lie algebras. Another cornerstone is the integration of categorical Calabi-Yau techniques, capturing the rich algebraic structure of these singularities. In this paper, we develop a systematic strategy to determine Namikawa-Weyl groups for representation spaces of Calabi-Yau-2 algebras, leveraging local-to-global functors, symmetry analysis, and $ A_{\infty} $-methods. Applying this approach to quiver varieties, we carry out the detailed calculations and recover Yaochen Wu's result. |
| title | Calabi-Yau techniques for Namikawa-Weyl groups |
| topic | Representation Theory Algebraic Geometry Symplectic Geometry 16G20 (Primary) 14J42, 53D30 (Secondary) |
| url | https://arxiv.org/abs/2501.03198 |