Linear structure on a finite Hecke category in type A
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911197955096576 |
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| author | Tolmachov, Kostiantyn |
| author_facet | Tolmachov, Kostiantyn |
| contents | For the group GL(n), we construct an action of the equivariant derived category of coherent sheaves on the Grothendieck-Springer resolution on a certain subcategory of a finite monodromic Hecke category. We use this to construct a partial categorification of the projection from the extened affine to the finite Hecke algebra of GL(n). As a crucial intermediate step, we compute the exterior powers, with respect to the perversely truncated multiplicative convolution, of a parabolic Springer sheaf corresponding to a maximal parabolic subgroup fixing a line in the defining n-dimensional representation of GL(n). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19734 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear structure on a finite Hecke category in type A Tolmachov, Kostiantyn Representation Theory Algebraic Geometry For the group GL(n), we construct an action of the equivariant derived category of coherent sheaves on the Grothendieck-Springer resolution on a certain subcategory of a finite monodromic Hecke category. We use this to construct a partial categorification of the projection from the extened affine to the finite Hecke algebra of GL(n). As a crucial intermediate step, we compute the exterior powers, with respect to the perversely truncated multiplicative convolution, of a parabolic Springer sheaf corresponding to a maximal parabolic subgroup fixing a line in the defining n-dimensional representation of GL(n). |
| title | Linear structure on a finite Hecke category in type A |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2403.19734 |