# Jacquet modules and local Langlands correspondence

## TL;DR

This paper explicitly computes the semisimplifications of Jacquet modules for irreducible representations with generic L-parameters of p-adic split odd special orthogonal and symplectic groups, using Moeglin's construction.

## Contribution

It provides explicit formulas for Jacquet modules in terms of standard modules, advancing understanding of local Langlands correspondence for these groups.

## Key findings

- Explicit semisimplification formulas for Jacquet modules
- Representation in terms of linear combinations of standard modules
- Application of Moeglin's explicit construction to tempered L-packets

## Abstract

In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them in terms of linear combinations of standard modules with rational coefficients. The main ingredient of this computation is to apply Moeglin's explicit construction of local A-packets to tempered L-packets.