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Transactions of the American Mathematical Society

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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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Article copyright: © Copyright 1986 American Mathematical Society