Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jalgebra.2007.06.018
Title: Degenerate principal series and local theta correspondence III: The case of complex groups
Authors: Lee, S.T. 
Zhu, C.-B. 
Keywords: Coinvariants
Degenerate principal series
Invariant distributions
Local theta correspondence
Reductive dual pair
Issue Date: 1-Jan-2008
Citation: Lee, S.T., Zhu, C.-B. (2008-01-01). Degenerate principal series and local theta correspondence III: The case of complex groups. Journal of Algebra 319 (1) : 336-359. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jalgebra.2007.06.018
Abstract: Let (G′, G) be one of the following complex dual pairs: (O (m, C), Sp (2 n, C)), (GL (m, C), GL (2 n, C)), (Sp (2 m, C), O (4 n, C)). We determine the relationship between the space of G′-coinvariants and certain degenerate principal series representations of G. We also show that the space of G′-invariant distributions is generated by the Dirac distribution as a G-representation. © 2007 Elsevier Inc. All rights reserved.
Source Title: Journal of Algebra
URI: http://scholarbank.nus.edu.sg/handle/10635/103112
ISSN: 00218693
DOI: 10.1016/j.jalgebra.2007.06.018
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