Howe quotients of unitary characters and unitary lowest weight modules

Loke, Hung Yean

doi:10.1090/S1088-4165-06-00279-2

Howe quotients of unitary characters and unitary lowest weight modules
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by Hung Yean Loke; with an Appendix by Soo Teck Lee

Represent. Theory 10 (2006), 21-47

DOI: https://doi.org/10.1090/S1088-4165-06-00279-2

Published electronically: January 9, 2006

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Abstract:

In this paper, let $(G,G’)$ be the dual pair $(\widetilde {\mathrm {Sp}}(p,\mathbb {R}), \tilde {\mathrm O}(n,m))$. We will determine the composition series of the Howe quotients of $G’$ which are lifts from one-dimensional unitary representations of $G$ and unitary lowest weight modules of $G$. We will also determine the unitarizability of the subquotients. Our method also works for the dual pairs $(\widetilde {\mathrm U}(p,q), \widetilde {\mathrm U}(n,m))$ and $(\tilde {\mathrm O}^*(2p), \widetilde {\mathrm {Sp}}(n,m))$.

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