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Transfers of K-types on local theta lifts of characters and unitary lowest weight modules |
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| Authors: | Hung Yean Loke Jia-Jun Ma U-Liang Tang |
| Institution: | 1. Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore 2. Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Be’er Sheva, 84105, Israel 3. School of Mathematics and Science, Singapore Polytechnic, 500 Dover Road, Singapore, 139651, Singapore |
| 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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