On the global Gan-Gross-Prasad conjecture for general spin groups

Abstract

We formulate a global Gan-Gross-Prasad conjecture for general spin groups. That is, we formulate a conjecture on a relation between periods of certain automorphic forms on $GSpi{n}_{n+1}\times GSpi{n}_n$ along the diagonal subgroup $GSpi{n}_n$ and some $L$-values. To support the conjecture, we show that the conjecture holds for $n=2$ and $3$ and for certain cases for $n=4$.

36 pages