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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Unitary quasilifting: applications

Author: Yuval Z. Flicker
Journal: Trans. Amer. Math. Soc. 294 (1986), 553-565
MSC: Primary 11F70; Secondary 22E55
MathSciNet review: 825721
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Abstract: Let $ U(3)$ be the quasi-split unitary group in three variables defined using a quadratic extension $ E/F$ of number fields. Complete local and global results are obtained for the $ \sigma $-endo-(unstable) lifting from $ U(2)$ to $ {\text{GL}}(3,\,E)$. This is used to establish quasi-(endo-)lifting for automorphic forms from $ U(2)$ to $ U(3)$ by means of base change from $ U(3)$ to $ {\text{GL}}(3,\,E)$. Base change quasi-lifting is also proven. Continuing the work of $ \left[ {\mathbf{I}} \right]$, the exposition is elementary, and uses only a simple form of an identity of trace formulas, and base change transfer of orbital integrals of spherical functions.

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