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Unitarizability in Corank Three for Classical $p$-adic Groups
About this Title
Marko Tadić
Publication: Memoirs of the American Mathematical Society
Publication Year:
2023; Volume 286, Number 1421
ISBNs: 978-1-4704-6283-3 (print); 978-1-4704-7515-4 (online)
DOI: https://doi.org/10.1090/memo/1421
Published electronically: May 16, 2023
Keywords: Non-archimedean local fields,
classical groups,
unitarizability
Table of Contents
Chapters
- 1. Introduction
- 2. Notation and Preliminary Results
- 3. Unitarizability in the Critical Case (Corank 1 and 2)
- 4. Unitarizability in the Critical Case (Corank 3, $\alpha >1$)
- 5. Remaining Cases for $\alpha =\frac 12$ and $\alpha =1$
- 6. The Case $\alpha =0$
- 7. Introductory Remarks on Unitarizability and Corank 2
- 8. Unitarizability in Corank 3
- 9. Unitarizability in Mixed Case for Corank $\leq 3$
- A. The Arthur Packet of $L(\nu ^{\alpha }\rho , \nu ^{\alpha -1}\rho ;\delta (\nu ^\alpha \rho ;\sigma ))$ by Colette Mœglin
- B. Jacquet Module of $L(\nu ^{\alpha }\rho , \nu ^{\alpha -1}\rho ;\delta (\nu ^\alpha \rho ;\sigma ))$
Abstract
Let $G$ be the $F$-points of a classical group defined over a $p$-adic field $F$ of characteristic $0$. We classify the irreducible unitarizable representation of $G$ that are subquotients of the parabolic induction of cuspidal representations of Levi subgroup of corank at most 3 in $G$.- James Arthur, The endoscopic classification of representations, American Mathematical Society Colloquium Publications, vol. 61, American Mathematical Society, Providence, RI, 2013. Orthogonal and symplectic groups. MR 3135650, DOI 10.1090/coll/061
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