Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments II: minimal sequences
Year: 2025
Type: article
Abstract: Let F be a non-Archimedean local field. For any irreducible smooth representation $$\pi $$ π of $$\textrm{GL}_n(F)$$ GL n ( F ) and a multisegment $${\mathfrak {m}}$$ m , we have an operation $$D_{{\mathfrak {m}}}(\pi )$$ D m ( π ) to construct a simple quotient $$\tau $$ τ of a Bernstein-Zelevinsky derivative of $$\pi $$ π . This article continues the previous one to study the following poset $$\begin{aligned} {\mathcal {S}}(\pi , \tau ) {:}{=}\left\{ {\mathfrak {n}} : D_{{\mathfrak {n}}}(\pi )\cong \tau \right\} , \end{aligned}$$ S ( π , τ ) : = n : D n ( π ) ≅ τ , where $${\mathfrak {n}}$$ n runs for all the multisegments. Here the partial ordering on $${\mathcal {S}}(\pi , \tau )$$ 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.
Source: manuscripta mathematica
Author: Kei Yuen Chan
Institution: University of Hong Kong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G5563306508, G6631915006, G7182346116
OpenAlex ID: W4416842216