Poles of intertwining operators in terms of irreducible components of Lusztig's characteristic variety in type A
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912544295223296 |
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| author | Droschl, Johannes |
| author_facet | Droschl, Johannes |
| contents | In this paper, we propose a conjectural formula for the order of the poles of intertwining operators in the context of the representation theory of general linear groups over $p$-adic fields. More specifically, we conjecturally relate the order of the pole to the dimension of a Hom-space associated with irreducible components of Lusztig's characteristic variety in type $A$. We verify the conjecture in a wide range of cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poles of intertwining operators in terms of irreducible components of Lusztig's characteristic variety in type A Droschl, Johannes Representation Theory Number Theory Quantum Algebra In this paper, we propose a conjectural formula for the order of the poles of intertwining operators in the context of the representation theory of general linear groups over $p$-adic fields. More specifically, we conjecturally relate the order of the pole to the dimension of a Hom-space associated with irreducible components of Lusztig's characteristic variety in type $A$. We verify the conjecture in a wide range of cases. |
| title | Poles of intertwining operators in terms of irreducible components of Lusztig's characteristic variety in type A |
| topic | Representation Theory Number Theory Quantum Algebra |
| url | https://arxiv.org/abs/2508.13817 |