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This is the second part of the authors’ work started from [JNQ08]. In this paper, we consider the complete relations among the local theta correspondence, local Langlands transfer, and the local descent attached to a given irreducible symplectic supercuspidal representation of p-adic GL2n. This is the natural extension of the work of Ginzburg-Rallis-Soudry ([GRS99]) and of Jiang-Soudry ([JS03]) on the local descents and the local Langlands transfers. The approach undertaken in this paper is purely local. A mixed approach with both local and global method, which works for more general classical groups, has been considered by JiangSoudry and was announced in [S08].

Symplectic supercuspidal representations of GL(2n) overp-adic fields