Abstract: | Period Problem is one of the most popular interesting problems in recently years, such as the Gan-Gross-Prasad conjectures. In this talk, we mainly focus on the local period problems, so called the relative local 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 a smooth representation of G(E). Assume the Langlands-Vogan conjecture, Prasad gives a precise description for the dimension \dim Hom_{G(F)}(\pi,\chi_G). We verify this conjecture if \pi is a discrete series representation and G=PGSp(4). |