LOCAL THETA CORRESPONDENCES FOR QUATERNIONIC DUAL PAIRS AND LANGLANDS PARAMETERS (Automorphic form, automorphic $L$-functions and related topics)

Abstract

This article is an announcement of a result of the author, which is based on the talk at the conference “Automorphic form, automorphic L-functions and related topics” at Research Institute for Mathematical Science on 26 January 2022. We describe local theta correspondence for quaternionic dual pair of almost equal rank in terms of Langlands parameter when the base field is ℝ and representations are discrete series.