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Remarks on the theta
correspondence over finite fields
Dongwen Liu and Zhicheng Wang |
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Vol. 306 (2020), No. 2, 587–609
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Abstract |
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S.-Y. Pan decomposed the uniform projection of the Weil representation of a finite symplectic-odd orthogonal dual pair, in terms of Deligne–Lusztig virtual characters, assuming that the order of the finite field is large enough. We use Pan’s decomposition to study the theta correspondence for dual pairs of this kind, following the approach of Adams and Moy and Aubert, Michel and Rouquier. Our results give the theta correspondence between unipotent representations and certain quadratic unipotent representations. |
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Keywords
theta correspondence, finite classical groups,
Deligne–Lusztig characters, unipotent cuspidal
representations
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Mathematical Subject Classification 2010
Primary: 20C33
Secondary: 22E50
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Milestones
Received: 16 August 2019
Revised: 13 December 2019
Accepted: 2 January 2020
Published: 13 July 2020
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Authors |
| Dongwen Liu | |
| School of Mathematical
Sciences Zhejiang University Hangzhou China |
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| Zhicheng Wang | |
| School of Mathematical
Sciences Zhejiang University Hangzhou China |
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