Nonvanishing of a certain sesquilinear form in the theta correspondence (Q2761187)
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scientific article; zbMATH DE number 1683067
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonvanishing of a certain sesquilinear form in the theta correspondence |
scientific article; zbMATH DE number 1683067 |
Statements
17 December 2001
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dual pair
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metaplectic representation
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Harish-Chandra module
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0.86770177
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0.8618023
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0.86096036
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0.8541726
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Nonvanishing of a certain sesquilinear form in the theta correspondence (English)
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In his paper [Commun. Contemp. Math. 2, 255-283 (2000; Zbl 0951.22008)], the author studied a certain sesquilinear form \((\;,\;)_\pi\) (introduced by Jian-Shu Li in 1989) for \(\pi\) in the semistable range of \(\theta(MO(p,q))\rightarrow MSp_{2n}(\mathbb{R})\), \(p+q\leq 2n+1\). In the paper under review the author shows that either \((\;,\;)_\pi\) or \((\;,\;)_{\pi\otimes \det}\) is nonvanishing. These results combined with a result of Przebinda suggest the existence of certain unipotent representations of \(Mp_{2n}(\mathbb{R})\) beyond the unitary representations of low rank.
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