Maffei's action and symplectic Springer action for quiver varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914733080182784 |
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| author | Wu, Yaochen |
| author_facet | Wu, Yaochen |
| contents | We examine the relationship between the actions of two Weyl groups on the cohomology of a smooth quiver variety: the Maffei's action of the Weyl group associated to the quiver, and the symplectic Springer action of the Namikawa-Weyl group of the affine quiver variety. We show there is a natural map from the former group to the latter, which is an embedding in favorable situations, and this map intertwines their actions on the cohomology. This answers a question raised in arXiv:1904.10497. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maffei's action and symplectic Springer action for quiver varieties Wu, Yaochen Representation Theory 16G20 We examine the relationship between the actions of two Weyl groups on the cohomology of a smooth quiver variety: the Maffei's action of the Weyl group associated to the quiver, and the symplectic Springer action of the Namikawa-Weyl group of the affine quiver variety. We show there is a natural map from the former group to the latter, which is an embedding in favorable situations, and this map intertwines their actions on the cohomology. This answers a question raised in arXiv:1904.10497. |
| title | Maffei's action and symplectic Springer action for quiver varieties |
| topic | Representation Theory 16G20 |
| url | https://arxiv.org/abs/2403.19823 |