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

This is part two of the authors' work on supercuspidal representations of GL(2n) over p-adic fields. 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 GL_2n. This is the natural extension of the work of Ginzburg, Rallis and Soudry and of Jiang and Soudry 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 methods, which works for more general classical groups, has been considered by Jiang and Soudry.