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, Prof. 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).
