TY - JOUR

T1 - Unramified whittaker functions on the metaplectic group

AU - Flicker, Yuval Z.

PY - 1987/11

Y1 - 1987/11

N2 - Kazhdan (unpublished), Shintani [Sh] and Casselman and Shalika [CS] computed explicitly the unramified Whittaker function of a quasisplit p-adic group.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,π ⊗π,) by Jacquet and Shalika [JS] (here π,π, are cuspidal GL(n, AF)-modules), and L(s,π, r) by [F] (here π is a cuspidal GL(n, AF)-module, E is a quadratic extension of the global field F, and r is the twisted tensor representation of the dual group of ResE/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 G of GL(n) (see [F', FK]).

AB - Kazhdan (unpublished), Shintani [Sh] and Casselman and Shalika [CS] computed explicitly the unramified Whittaker function of a quasisplit p-adic group.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,π ⊗π,) by Jacquet and Shalika [JS] (here π,π, are cuspidal GL(n, AF)-modules), and L(s,π, r) by [F] (here π is a cuspidal GL(n, AF)-module, E is a quadratic extension of the global field F, and r is the twisted tensor representation of the dual group of ResE/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 G of GL(n) (see [F', FK]).

UR - http://www.scopus.com/inward/record.url?scp=84968480675&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1987-0908643-7

DO - 10.1090/S0002-9939-1987-0908643-7

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AN - SCOPUS:84968480675

SN - 0002-9939

VL - 101

SP - 431

EP - 435

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -