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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Unramified Whittaker functions on the metaplectic group

Author: Yuval Z. Flicker
Journal: Proc. Amer. Math. Soc. 101 (1987), 431-435
MSC: Primary 11F70; Secondary 22E50
MathSciNet review: 908643
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Abstract: Kazhdan (unpublished), Shintani [Sh] and Casselman and Shalika [CS] computed explicitly the unramified Whittaker function of a quasisplit $ p$-adic group. This is the main local ingredient used in the Rankin-Selberg-Shimura method, which yielded interesting results in the study of Euler products such as $ L(s,\pi \otimes \pi ')$ by Jacquet and Shalika [JS] (here $ \pi ,\pi '$ are cuspidal $ GL(n,{A_F})$-modules), and $ L(s,\pi ,r)$ by [F] (here $ \pi $ is a cuspidal $ GL(n,{A_E})$-module, $ E$ is a quadratic extension of the global field $ F$, and $ r$ is the twisted tensor representation of the dual group of $ \operatorname{Res}_{E/F}GL(n))$. Our purpose here is to generalize Shintani's computation [Sh] from the context of $ GL(n)$ to that of the metaplectic $ r$-fold covering group $ \tilde G$ of $ GL(n)$ (see $ [{\mathbf{F'}},{\mathbf{FK}}]$).

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