Twisted automorphic descent
Applying Arthur’s endoscopic classification of discrete automorphic representations for classical groups, we extend Ginzburg-Rallis-Soudry’s automorphic descent from quasi-split classical groups setting to their pure inner forms.
Combining with the multiplicity-free results of local Gan-Gross-Prasad conjecture, we not just provide a concrete module construction of cuspidal automorphic representations from the sauce representations of general linear groups, but also prove one direction of global Gan-Gross-Prasad conjecture. Moreover, our study leads us to many fundamental questions on the Fourier coefficients of automorphic forms, which connect to the existence of nonvanishing twist central value of L-functions for instance.
