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.
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