Transfers of \(K\)-types on local theta lifts of characters and unitary lowest weight modules
type: Item
instance of: scholarly article
title: Transfers of \(K\)-types on local theta lifts of characters and unitary lowest weight modules
zbMATH Open document ID: 1301.22009
author: Jia-Jun Ma
author: U-Liang Tang
author: Hung Yean Loke
published in: Israel Journal of Mathematics
publication date: 2014-10-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1207.6451
review text: The authors study representations of the indefinite orthogonal group \(O(n,m)\) which are local theta lifts of one-dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. They apply the transfer of \(K\)-types on these representations of \(O(n,m)\). Introducing the Harish-Chandra module \(\theta_p^{n,m}(1)\) of \(O(n,m)\), they consider \(K_{n,m}=O(n)\times O(m)\), a maximal compact subgroup of \(O(n,m)\), and the \(K_{n,m}\)-types of \(\theta_p^{n,m}(1)\). Another ingredient is the subgroup \(O(n)\times O(r)\otimes O(m-r)\) of \(K_{n,m}\) and the restriction of \(\theta_p^{n,m}(1)\). With these objects, they apply the transfer of \(K\)-types due to Enright and Wallach (see, e.g., [\textit{T. Enright} et al., Prog. Math. 40, 97--143 (1983; Zbl 0535.22012)] and study their effects on the dual pair correspondences. Finally, they also use these results to study subquotients of some cohomologically induced modules. The techniques presented in this paper can be applied to \(U(n,m)\) and \(Sp(n,m)\).
reviewed by: Panagiotis Batakidis
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 6361292
MaRDI profile type: Publication
OpenAlex ID: W2059000708
arXiv ID: 1207.6451
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DOI: 10.1007/S11856-014-1061-8
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description: scientific article; zbMATH DE number 6361292