On Jacquet modules of representations of segment type
Ivan Matic, Marko Tadic

TL;DR
This paper provides a comprehensive analysis of Jacquet modules for segment-type representations of Sp(n) and SO(2n+1, F), crucial for understanding discrete series in non-archimedean local fields.
Contribution
It offers a complete description of Jacquet modules for these representations and introduces an alternative method for strongly positive discrete series.
Findings
Complete description of Jacquet modules for segment-type representations
New method for determining Jacquet modules of strongly positive discrete series
Description of top Jacquet modules of general discrete series
Abstract
We study representations of segment type of groups Sp(n) and SO(2n+1, F) over a local non-archimedean field, which play a fundamental role in the constructions of discrete series, and obtain a complete description of the Jacquet modules of these representations. Also, we provide an alternative way for determination of Jacquet modules of strongly positive discrete series and a description of top Jacquet modules of general discrete series. In this version are corrected few typographical errors which exist in the published version of this paper (see page 5 of the paper for more details).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Mathematical Analysis and Transform Methods · Algebraic Geometry and Number Theory
