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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.00667 |
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| _version_ | 1866908744424620032 |
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| author | Chan, Kei Yuen |
| author_facet | Chan, Kei Yuen |
| contents | Let $F$ be a non-Archimedean local field. For any irreducible smooth representation $π$ of $\mathrm{GL}_n(F)$ and a multisegment $\mathfrak m$, we have an operation $D_{\mathfrak m}(π)$ to construct a simple quotient $τ$ of a Bernstein-Zelevinsky derivative of $π$. This article continues the previous one to study the following poset \[ \mathcal S(π, τ) :=\left\{ \mathfrak n : D_{\mathfrak n}(π)\cong τ\right\} , \] where $\mathfrak n$ runs for all the multisegments. Here the partial ordering on $\mathcal S(π, τ)$ comes from the Zelevinsky ordering. We show that the poset has a unique minimal multisegment. Along the way, we introduce two new ingredients: fine chain orderings and local minimizability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00667 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments II: Minimal sequences Chan, Kei Yuen Representation Theory Let $F$ be a non-Archimedean local field. For any irreducible smooth representation $π$ of $\mathrm{GL}_n(F)$ and a multisegment $\mathfrak m$, we have an operation $D_{\mathfrak m}(π)$ to construct a simple quotient $τ$ of a Bernstein-Zelevinsky derivative of $π$. This article continues the previous one to study the following poset \[ \mathcal S(π, τ) :=\left\{ \mathfrak n : D_{\mathfrak n}(π)\cong τ\right\} , \] where $\mathfrak n$ runs for all the multisegments. Here the partial ordering on $\mathcal S(π, τ)$ comes from the Zelevinsky ordering. We show that the poset has a unique minimal multisegment. Along the way, we introduce two new ingredients: fine chain orderings and local minimizability. |
| title | Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments II: Minimal sequences |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.00667 |