On a pairing of Goldberg-Shahidi for even orthogonal groups
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- by Wen-Wei Li
- Represent. Theory 17 (2013), 337-381
- DOI: https://doi.org/10.1090/S1088-4165-2013-00435-1
- Published electronically: June 17, 2013
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Abstract:
Let $\pi \otimes \sigma$ be a supercuspidal representation of $\mathrm {GL}(2n) \times \mathrm {SO}(2n)$ over a $p$-adic field with $\pi$ selfdual, where $\mathrm {SO}(2n)$ stands for a quasisplit even special orthogonal group. In order to study its normalized parabolic induction to $\mathrm {SO}(6n)$, Goldberg and Shahidi defined a pairing $R$ between the matrix coefficients of $\pi$ and $\sigma$ which controls the residue of the standard intertwining operator. The elliptic part $R_\text {ell}$ of $R$ is conjectured to be related to twisted endoscopic transfer. Based on Arthur’s endoscopic classification and Spallone’s improvement of Goldberg-Shahidi program, we will verify some of their predictions for general $n$, under the assumption that $\pi$ does not come from $\mathrm {SO}(2n+1)$.References
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Bibliographic Information
- Wen-Wei Li
- Affiliation: Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences 55, Zhongguancun East Road, 100190 Beijing, China
- Email: wwli@math.ac.cn
- Received by editor(s): June 1, 2012
- Received by editor(s) in revised form: December 6, 2012, and January 6, 2013
- Published electronically: June 17, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory 17 (2013), 337-381
- MSC (2010): Primary 22E50; Secondary 11F70
- DOI: https://doi.org/10.1090/S1088-4165-2013-00435-1
- MathSciNet review: 3067291