A stacky generalized Springer correspondence and rigid enhancements of L-parameters
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909219994730496 |
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| author | Dillery, Peter Schwein, David |
| author_facet | Dillery, Peter Schwein, David |
| contents | Motivated by applications to the Langlands program, Aubert-Moussaoui-Solleveld extended Lusztig's generalized Springer correspondence to disconnected reductive groups. We use stacks to give a more geometric account of their theory, in particular, formulating a truly geometric version of the (relevant analogue of the) Bernstein-Zelevinsky Geometrical Lemma and explaining how to compare the correspondence on the group and the Lie algebra using quasi-logarithms. As an application, we study Kaletha's rigid enhancements of L-parameters and draw the same conclusions as Aubert-Moussaoui-Solleveld for this enhancement: there exists a cuspidal support map and its fibers are parameterized by irreducible representations of twisted group algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11752 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A stacky generalized Springer correspondence and rigid enhancements of L-parameters Dillery, Peter Schwein, David Representation Theory Number Theory 11S37, 20Gxx, 22E50, 17B08 Motivated by applications to the Langlands program, Aubert-Moussaoui-Solleveld extended Lusztig's generalized Springer correspondence to disconnected reductive groups. We use stacks to give a more geometric account of their theory, in particular, formulating a truly geometric version of the (relevant analogue of the) Bernstein-Zelevinsky Geometrical Lemma and explaining how to compare the correspondence on the group and the Lie algebra using quasi-logarithms. As an application, we study Kaletha's rigid enhancements of L-parameters and draw the same conclusions as Aubert-Moussaoui-Solleveld for this enhancement: there exists a cuspidal support map and its fibers are parameterized by irreducible representations of twisted group algebras. |
| title | A stacky generalized Springer correspondence and rigid enhancements of L-parameters |
| topic | Representation Theory Number Theory 11S37, 20Gxx, 22E50, 17B08 |
| url | https://arxiv.org/abs/2308.11752 |