Degenerate principal series and local theta correspondence III: The case of complex groups

JOURNAL OF ALGEBRA

卷:319

Article

Lee, Soo Teck¹  Zhu, Chen-Bo¹ 

[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

关键词: reductive dual pair;    local theta correspondence;    degenerate principal series;    coinvariants;    invariant distributions;   

DOI  :  10.1016/j.jalgebra.2007.06.018

来源: Elsevier

【 摘 要 】

Let (G', G) be one of the following complex dual pairs: (O(m, C), Sp(2n, C), (GL(m, C), GL(2n, C), (Sp(2m, C), O(4n, 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. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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