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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2302.03492 |
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| _version_ | 1866929233265164288 |
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| author | Prasad, Dipendra |
| author_facet | Prasad, Dipendra |
| contents | In this mostly expository article, we consider certain homological aspects of branching laws for representations of a group restricted to its subgroups in the context of $p$-adic groups. We follow our earlier paper, ICM 2018 proceedings, updating it with some more recent works. In particular, following Chan and Chan-Savin, see many of their papers listed in the bibliography, we have emphasized in this work that the restriction of a (generic) representation $π$ of a group $G$ to a closed subgroup $H$ (most of the paper is written in the context of GGP) turns out to be a projective representation on most Bernstein blocks of the category of smooth representations of $H$. Further, once $π|_H$ is a projective module in a particular Bernstein block, it has a simple structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03492 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homological aspects of branching laws Prasad, Dipendra Representation Theory 11F70, 22E55 In this mostly expository article, we consider certain homological aspects of branching laws for representations of a group restricted to its subgroups in the context of $p$-adic groups. We follow our earlier paper, ICM 2018 proceedings, updating it with some more recent works. In particular, following Chan and Chan-Savin, see many of their papers listed in the bibliography, we have emphasized in this work that the restriction of a (generic) representation $π$ of a group $G$ to a closed subgroup $H$ (most of the paper is written in the context of GGP) turns out to be a projective representation on most Bernstein blocks of the category of smooth representations of $H$. Further, once $π|_H$ is a projective module in a particular Bernstein block, it has a simple structure. |
| title | Homological aspects of branching laws |
| topic | Representation Theory 11F70, 22E55 |
| url | https://arxiv.org/abs/2302.03492 |