Bernstein degree and associated cycles of Harish-Chandra modules -- Hermitian symmetric case -- (Q2740889)
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scientific article; zbMATH DE number 1641598
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bernstein degree and associated cycles of Harish-Chandra modules -- Hermitian symmetric case -- |
scientific article; zbMATH DE number 1641598 |
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5 September 2001
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unitary representations
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symmetric spaces
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Bernstein degree
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Bernstein degree and associated cycles of Harish-Chandra modules -- Hermitian symmetric case -- (English)
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In the present article, the Bernstein degrees and the associated cycles of the irreducible unitary highest weight representations of the metaplectic double cover of \(Sp (2n, R)\), \(U (p,q)\) or \(O^* (2p)\) are studied, by using the theta correspondence of dual pairs. The main result is the determination of the associated cycles of singular unitary highest weight representations, which are the theta lifts of irreducible representations of certain compact subgroups.NEWLINENEWLINEFor the entire collection see [Zbl 0968.22001].
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