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Title: Tensor product of degenerate principal series and local theta correspondence
Authors: Li, J.-S.
Tan, E.-C. 
Zhu, C.-B. 
Keywords: Complementary series
Degenerate principal series
Local theta correspondence
Reductive dual pair
Zeta integral
Issue Date: 10-Nov-2001
Citation: Li, J.-S., Tan, E.-C., Zhu, C.-B. (2001-11-10). Tensor product of degenerate principal series and local theta correspondence. Journal of Functional Analysis 186 (2) : 381-431. ScholarBank@NUS Repository.
Abstract: We construct an intertwining map from the oscillator representation to the tensor product of two degenerate principal series of G and G1 which form a reductive dual pair in the sense of Howe. We derive results on local theta correspondence for the dual pairs (O(p, q), Sp(2q, ℝ)). (U(p, q), U(q, q)) and (Sp(p, q), O*(4q)). where p ≥ q. We also describe the correspondence completely for the pairs (O(p, q), SL(2, ℝ)), (U(p, q) U(1,1)), and (Sp(p, q), O*(4)). © 2001 Academic Press.
Source Title: Journal of Functional Analysis
ISSN: 00221236
DOI: 10.1006/jfan.2001.3786
Appears in Collections:Staff Publications

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