School of Mathematics Colloquium

# The Prasad conjecture for PGSp(4)

## by Dr. Hengfei Lu (TIFR, Mumbai)

Thursday, November 16, 2017 from to (Asia/Kolkata)
at TIFR, Mumbai ( AG-69 )
 Description 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).  Material: