Nearby Cycle Sheaves for Stable Polar Representations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866918143478202368 |
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| author | Grinberg, Mikhail Vilonen, Kari Xue, Ting |
| author_facet | Grinberg, Mikhail Vilonen, Kari Xue, Ting |
| contents | Let G|V, G connected, reductive over C, be a stable polar representation in the sense of [DK], satisfying some mild additional hypotheses. Given a G-equivariant rank one local system L on the general fiber of the quotient map f : V --> V/G, we compute the Fourier transform of the corresponding nearby cycle sheaf P on the zero-fiber of f. This provides a partial generalization of the results of [Gr1] and [GVX1]. Our main intended application is to the theory of character sheaves for graded Lie algebras over C. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_14522 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nearby Cycle Sheaves for Stable Polar Representations Grinberg, Mikhail Vilonen, Kari Xue, Ting Algebraic Geometry Representation Theory 14D05 (primary), 22E46 (secondary) Let G|V, G connected, reductive over C, be a stable polar representation in the sense of [DK], satisfying some mild additional hypotheses. Given a G-equivariant rank one local system L on the general fiber of the quotient map f : V --> V/G, we compute the Fourier transform of the corresponding nearby cycle sheaf P on the zero-fiber of f. This provides a partial generalization of the results of [Gr1] and [GVX1]. Our main intended application is to the theory of character sheaves for graded Lie algebras over C. |
| title | Nearby Cycle Sheaves for Stable Polar Representations |
| topic | Algebraic Geometry Representation Theory 14D05 (primary), 22E46 (secondary) |
| url | https://arxiv.org/abs/2012.14522 |