Lectures on local theta correspondence
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914244195254272 |
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| author | Zhu, Chen-Bo |
| author_facet | Zhu, Chen-Bo |
| contents | This set of lecture notes on local theta correspondence is the written version of a mini-course the author gave in March of 2025 for the program ``Representation Theory and Noncommutative Geometry" at the Institut Henri Poincaré, Paris. The emphasis is on the Archimedean theory, which concerns representations of classical Lie groups. Section 1 is about the basic theory, including Howe's Duality Theorem, and the conservation relations. Section 2 highlights the invariant-theoretic nature of local theta correspondence via the proof of the conservation relations. Sections 3 and 4 explain how two fundamental invariants of representations behave under local theta correspondence. The final section discusses applications to unitary representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lectures on local theta correspondence Zhu, Chen-Bo Representation Theory 22E45, 22E46 This set of lecture notes on local theta correspondence is the written version of a mini-course the author gave in March of 2025 for the program ``Representation Theory and Noncommutative Geometry" at the Institut Henri Poincaré, Paris. The emphasis is on the Archimedean theory, which concerns representations of classical Lie groups. Section 1 is about the basic theory, including Howe's Duality Theorem, and the conservation relations. Section 2 highlights the invariant-theoretic nature of local theta correspondence via the proof of the conservation relations. Sections 3 and 4 explain how two fundamental invariants of representations behave under local theta correspondence. The final section discusses applications to unitary representation theory. |
| title | Lectures on local theta correspondence |
| topic | Representation Theory 22E45, 22E46 |
| url | https://arxiv.org/abs/2511.07849 |