Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments I: reduction to combinatorics
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866916514764947456 |
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| author | Chan, Kei Yuen |
| author_facet | Chan, Kei Yuen |
| contents | Let $F$ be a local non-Archimedean field. A sequence of derivatives of generalized Steinberg representations can be used to construct simple quotients of Bernstein-Zelevinsky derivatives of irreducible representations of $\mathrm{GL}_n(F)$. In the first of a series of articles, we introduce a notion of a highest derivative multisegment, which in turn gives a combinatorial approach to study problems about those simple quotients. We also prove a double derivative result along the way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_13286 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments I: reduction to combinatorics Chan, Kei Yuen Representation Theory Number Theory 11F70, 22E50, 20C08 Let $F$ be a local non-Archimedean field. A sequence of derivatives of generalized Steinberg representations can be used to construct simple quotients of Bernstein-Zelevinsky derivatives of irreducible representations of $\mathrm{GL}_n(F)$. In the first of a series of articles, we introduce a notion of a highest derivative multisegment, which in turn gives a combinatorial approach to study problems about those simple quotients. We also prove a double derivative result along the way. |
| title | Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments I: reduction to combinatorics |
| topic | Representation Theory Number Theory 11F70, 22E50, 20C08 |
| url | https://arxiv.org/abs/2111.13286 |