We use the theta correspondence between GSp4(E) and GO(V) to study the GSp4-distinction problems over a quadratic extension E/F of nonarchimedean local fields of characteristic 0. With a similar strategy, we investigate the distinction problem for the pair (GSp4(E); GSp1,1(F)), where GSp1,1 is the unique inner form of GSp4 defined over F. Then we verify the Prasad conjecture for a discrete series representation τ of PGSp4(E).
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Langlands correspondence
- Quaternionic hermitian groups
- See-saw diagrams
- The prasad conjecture
- Theta lift