Pointwise purity, derived Satake, and Symplectic duality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914001644945408 |
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| author | Ginzburg, Victor |
| author_facet | Ginzburg, Victor |
| contents | It has been known for a long time that Ext's between IC-sheaves may often be expressed in terms of Hom's between cohomology groups. We prove a more general result under weaker assumptions. The result is used to describe the action of the derived Satake equivalence on !-pure objects and show that the equivalence enjoys a new kind of functoriality with respect to morphisms of reductive groups. We find and prove normality of the symplectic dual X^! for many smooth affine Hamiltonian G-varieties X, including X=T^*(G/H) for all connected reductive subgroups H of G. We also describe the symplectic duals M^! in the case of Coulomb branches and prove that M^! has symplectic singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pointwise purity, derived Satake, and Symplectic duality Ginzburg, Victor Representation Theory It has been known for a long time that Ext's between IC-sheaves may often be expressed in terms of Hom's between cohomology groups. We prove a more general result under weaker assumptions. The result is used to describe the action of the derived Satake equivalence on !-pure objects and show that the equivalence enjoys a new kind of functoriality with respect to morphisms of reductive groups. We find and prove normality of the symplectic dual X^! for many smooth affine Hamiltonian G-varieties X, including X=T^*(G/H) for all connected reductive subgroups H of G. We also describe the symplectic duals M^! in the case of Coulomb branches and prove that M^! has symplectic singularities. |
| title | Pointwise purity, derived Satake, and Symplectic duality |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2508.15958 |