Transfer of K-types on local theta lifts of characters and unitary lowest weight modules

TL;DR

This paper investigates how transfer of K-types affects local theta lifts of characters and lowest weight modules for indefinite orthogonal groups, demonstrating compatibility and exploring implications for cohomologically induced modules.

Contribution

It introduces the transfer of K-types to local theta lifts of specific representations and shows their compatibility with dual pair correspondences.

Findings

Transfer of K-types is compatible with theta lifting.

Provides explicit examples of this compatibility.

Uses results to analyze subquotients of cohomologically induced modules.

Abstract

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer of K-types on these representations of O(n,m), and we study their effects on the dual pair correspondences. These results provide examples that the theta lifting is compatible with the transfer of K-types. Finally we will use these results to study subquotients of some cohomologically induced modules.