Citation
Js. Li et al., Tensor product of degenerate principal series and local theta correspondence, J FUNCT ANA, 186(2), 2001, pp. 381-431
Citations number
24
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN journal
00221236
→ ACNP
Volume
186
Issue
2
Year of publication
2001
Pages
381 - 431
Database
ISI
SICI code
0022-1236(20011110)186:2<381:TPODPS>2.0.ZU;2-D
Abstract
We construct an intertwining map from the oscillator representation to the
tensor product of two degenerate principal series of G and G' 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 greater than or equal to q. We also describ
e the correspondence completely for the pairs (O(p, q), SL(2, R)),(U(p,q)U(
1, 1)), and (Sp(p,q),O*(4)). (C) 2001 Academic Press.