Pull-back and push-forward functors for holonomic modules over Cherednik algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909122697363456 |
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| author | Bellamy, Gwyn Etingof, Pavel Thompson, Daniel |
| author_facet | Bellamy, Gwyn Etingof, Pavel Thompson, Daniel |
| contents | In this article we continue the study of holonomic modules over sheaves of Cherednik algebras, initiated by the third author in [Tho18]. Working with arbitrary parameters, we first develop a theory of $b$-functions to prove that push-forward along open embeddings preserves holonomicity. This implies that pull-back along closed embeddings also preserves holonomicity. We use these facts to show that both push-forward and pull-back under any melys morphism preserves holonomicity. Since duality preserves holonomicity, we deduce that extraordinary push-forward and extraordinary pull-back also exist for holonomic modules.
As a consequence, we give a general classification of irreducible holonomic modules similar to the classification of irreducible holonomic $\mathscr{D}$-modules as minimal extensions of integrable connections on locally closed subsets. Finally, we prove that ext-groups between holonomic modules are finite-dimensional and explore applications of our work to the classification of aspherical parameters and existence of finite-dimensional modules for sheaves of Cherednik algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pull-back and push-forward functors for holonomic modules over Cherednik algebras Bellamy, Gwyn Etingof, Pavel Thompson, Daniel Quantum Algebra Algebraic Geometry Representation Theory In this article we continue the study of holonomic modules over sheaves of Cherednik algebras, initiated by the third author in [Tho18]. Working with arbitrary parameters, we first develop a theory of $b$-functions to prove that push-forward along open embeddings preserves holonomicity. This implies that pull-back along closed embeddings also preserves holonomicity. We use these facts to show that both push-forward and pull-back under any melys morphism preserves holonomicity. Since duality preserves holonomicity, we deduce that extraordinary push-forward and extraordinary pull-back also exist for holonomic modules. As a consequence, we give a general classification of irreducible holonomic modules similar to the classification of irreducible holonomic $\mathscr{D}$-modules as minimal extensions of integrable connections on locally closed subsets. Finally, we prove that ext-groups between holonomic modules are finite-dimensional and explore applications of our work to the classification of aspherical parameters and existence of finite-dimensional modules for sheaves of Cherednik algebras. |
| title | Pull-back and push-forward functors for holonomic modules over Cherednik algebras |
| topic | Quantum Algebra Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2402.18210 |