The Prasad conjecture

Period Problem is one of the most popular interesting problems in recent years, such as the Gan-Gross-Prasad conjectures. In this talk, we mainly focus on the local period problems, so called the relative Langlands programs. Given a quadratic local field extension E/F and a quasi-split reductive group G defined over F with associated quadratic character $\chi_G$, let $\pi$ be an irreducible admissible representation of G(E). Assume the Langlands-Vogan conjecture. Dipendra Prasad uses the enhanced L-parameter of $\pi$ to give a precise description for the multiplicity $\dim Hom_{G(F)}(\pi,\chi_G)$ if the L-packet $\Pi_\pi$ contains a generic representation. Then we can verify this conjecture if G=GSp(4).