A Betti geometric Casselman-Shalika equivalence
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915908389175296 |
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| author | Sandvik, Colton |
| author_facet | Sandvik, Colton |
| contents | Whittaker sheaves are ubiquitous in geometric representation theory; however, their definition requires one to restrict the sheaf-theoretic setting to either étale sheaves or $D$-modules. Gaitsgory and Lysenko proposed a solution to this problem called the Kirillov model, which is well-defined for many sheaf theories. In this paper, we advance the study of the Kirillov model in the setting of Betti sheaves with a particular emphasis on developing a theory of Iwahori-Whittaker sheaves on the affine Grassmannian. Using this framework, we prove a Betti geometric Casselman-Shalika equivalence, which relates Iwahori-Whittaker perverse sheaves on the affine Grassmannian with the Satake category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01423 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Betti geometric Casselman-Shalika equivalence Sandvik, Colton Representation Theory Whittaker sheaves are ubiquitous in geometric representation theory; however, their definition requires one to restrict the sheaf-theoretic setting to either étale sheaves or $D$-modules. Gaitsgory and Lysenko proposed a solution to this problem called the Kirillov model, which is well-defined for many sheaf theories. In this paper, we advance the study of the Kirillov model in the setting of Betti sheaves with a particular emphasis on developing a theory of Iwahori-Whittaker sheaves on the affine Grassmannian. Using this framework, we prove a Betti geometric Casselman-Shalika equivalence, which relates Iwahori-Whittaker perverse sheaves on the affine Grassmannian with the Satake category. |
| title | A Betti geometric Casselman-Shalika equivalence |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2604.01423 |