Jacquet modules and local Langlands correspondence

摘要

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 M oe glin's explicit construction of local A-packets to tempered L-packets. Finally, we study the derivatives introduced by Minguez.