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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/2602.08637 |
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| _version_ | 1866912890722713600 |
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| author | Wen, Xueqing Wen, Yaoxiong |
| author_facet | Wen, Xueqing Wen, Yaoxiong |
| contents | We introduce minimal Richardson orbits and pseudo-polarizations for nilpotent orbits in classical Lie algebras of types B, C, and D. For any nilpotent orbit, we classify all minimal Richardson orbits containing it and thereby determine the associated pseudo-polarizations. We prove that the corresponding Spaltenstein varieties are smooth and pure dimensional, with iterated orthogonal/isotropic Grassmannian fibrations. As an application, we extend the seesaw property and duality of Fu-Ruan-Wen from Richardson orbits to all special orbits in types B and C. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08637 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spaltenstein Varieties Associated with Pseudo-Polarizations Wen, Xueqing Wen, Yaoxiong Algebraic Geometry Representation Theory We introduce minimal Richardson orbits and pseudo-polarizations for nilpotent orbits in classical Lie algebras of types B, C, and D. For any nilpotent orbit, we classify all minimal Richardson orbits containing it and thereby determine the associated pseudo-polarizations. We prove that the corresponding Spaltenstein varieties are smooth and pure dimensional, with iterated orthogonal/isotropic Grassmannian fibrations. As an application, we extend the seesaw property and duality of Fu-Ruan-Wen from Richardson orbits to all special orbits in types B and C. |
| title | Spaltenstein Varieties Associated with Pseudo-Polarizations |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2602.08637 |