Spherical Functions in a Certain Distinguished Model

J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 3, Page 369--400.

Takano, Keiji
Spherical Functions in a Certain Distinguished Model
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Abstract:
We study unramified principal series representations of general linear groups over p-adic fields, distinguished with respect to the fixator of the Galois involution. We give a certain condition for the unramified principal series to be distinguished, and give a formula for spherical vectors in the distinguished models of $GL_n$, following the method of Kato and Hironaka. We give explicit results for $GL_2$ and $GL_3$.

Mathematics Subject Classification (1991): Primary 11F70; Secondary 22E35
Mathematical Reviews Number: MR1792733

Received: 1999-03-18