Local theta correspondences and Langlands parameters for rigid inner twists

Abstract

In this paper, we formulate a conjecture that describes the local theta correspondences in terms of the local Langland correspondences for rigid inner twists, which contain the correspondences for quaternionic dual pairs. Moreover, we verify the conjecture holds in some specific cases.

In version 1, the author pointed out an error in a paper [Ike19] of Ikematsu. However, it turned out that the pointing is incorrect. I would like to take this opportunity to apologize