Dynkin abelianisations of flag varieties
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909163214340096 |
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| author | Enugandla, Shreepranav Varma Fang, Xin Fourier, Ghislain Steinert, Christian |
| author_facet | Enugandla, Shreepranav Varma Fang, Xin Fourier, Ghislain Steinert, Christian |
| contents | Cerulli Irelli and Lanini have shown that PBW degenerations of flag varieties in type A and C are actually Schubert varieties of higher rank. We introduce Dynkin cones to parameterise specific abelianisations of classical Lie algebras. Within this framework, we generalise their result to all degenerations of flag varieties defined by degree vectors originating from a Dynkin cone. This framework allows us to determine the extent to which a flag variety can be degenerate while still naturally being a Schubert variety of the same Lie type. Furthermore, we compute the defining relations for the corresponding degenerate simple modules in all classical types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynkin abelianisations of flag varieties Enugandla, Shreepranav Varma Fang, Xin Fourier, Ghislain Steinert, Christian Representation Theory Algebraic Geometry Rings and Algebras 17B10, 14D06, 14M15 Cerulli Irelli and Lanini have shown that PBW degenerations of flag varieties in type A and C are actually Schubert varieties of higher rank. We introduce Dynkin cones to parameterise specific abelianisations of classical Lie algebras. Within this framework, we generalise their result to all degenerations of flag varieties defined by degree vectors originating from a Dynkin cone. This framework allows us to determine the extent to which a flag variety can be degenerate while still naturally being a Schubert variety of the same Lie type. Furthermore, we compute the defining relations for the corresponding degenerate simple modules in all classical types. |
| title | Dynkin abelianisations of flag varieties |
| topic | Representation Theory Algebraic Geometry Rings and Algebras 17B10, 14D06, 14M15 |
| url | https://arxiv.org/abs/2404.05277 |