A note on the local theta correspondence for unitary similitude dual pairs

TL;DR

This paper investigates the local theta correspondence for unitary similitude dual pairs over p-adic fields, extending Roberts' work on orthogonal-symplectic pairs to a new setting.

Contribution

It introduces new insights into the local theta correspondence specifically for unitary similitude dual pairs over p-adic fields, expanding the theoretical framework.

Findings

Extended Roberts' results to unitary similitude dual pairs

Provided new theoretical understanding of local theta correspondence

Potential implications for representation theory over p-adic fields

Abstract

Following Roberts' work in the case of orthogonal-symplectic similitude dual pairs, we study the local theta correspondence for unitary similitude dual pairs over a $p$-adic field.