Parameters and Theta lifts

TL;DR

This paper clarifies the relationship between Harish-Chandra and Langlands-Vogan parameters for real symplectic and orthogonal groups, and applies this to reformulate known results on the Howe correspondence for dual pairs.

Contribution

It explicitly establishes the correspondence between two types of parameters and reformulates existing results using this new perspective.

Findings

Explicit correspondence between Harish-Chandra and Langlands-Vogan parameters

Reformulation of Moeglin's and Paul's results on Howe correspondence

Enhanced understanding of dual pairs in real symplectic and orthogonal groups

Abstract

In this note, we make explicit the correspondence between Harish-Chandra parameters and Langlands-Vogan parameters for symplectic groups and orthogonal groups of equal rank over reals. As an application, we reformulate Moeglin's results and Paul's work on the Howe correspondence for symplectic-orthogonal dual pairs using Langlands-Vogan parameters.