Chen Wan, Rutgers University, Newark, New JerseyLei Zhang, National University of Singapore, Singapore

• 1. Introduction and main results2. The strategy3. The model $({\mathrm {GSp}}_6\times {\mathrm {GSp}}_4,({\mathrm {GSp}}_4\times {\mathrm {GSp}}_2)^0)$4. The model $({\mathrm {GL}}_4\times {\mathrm {GL}}_2,{\mathrm {GL}}_2\times {\mathrm {GL}}_2)$5. The model $({\mathrm {GL}}_6,{\mathrm {GL}}_2\ltimes U)$6. The models $({\mathrm {GU}}_6,{\mathrm {GU}}_2\ltimes U)$ and $({\mathrm {GU}}_4\times {\mathrm {GU}}_2,({\mathrm {GU}}_2\times {\mathrm {GU}}_2)^0)$7. The model $(E_7,{\mathrm {PGL}}_2\ltimes U)$8. The remaining models9. Local multiplicity