The Generalized Whittaker Functions for $SU(2,1)$ and the Fourier Expansion of Automorphic Forms

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The Generalized Whittaker Functions for $SU(2,1)$ and the Fourier Expansion of Automorphic Forms

J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 3, Page 477--526.

Ishikawa, Yoshi-hiro
The Generalized Whittaker Functions for $SU(2,1)$ and the Fourier Expansion of Automorphic Forms
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Abstract:
Explicit form of Fourier expansion of automorphic forms plays an important role in the theory. Here we investigate the case of

$SU(2,1)$ and give an explicit formula of generalized Whittaker functions for the standard representations of the group. Together with a result of [K-O], we obtain a form of fully developed Fourier expansion of automorphic forms belonging to arbitrary standard representations.

Mathematics Subject Classification (1991): Primary 11F70; Secondary 11F30, 22E30, 33C15

Mathematical Reviews Number: MR1726680

Received: 1998-11-13

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The Generalized Whittaker Functions for SU(2,1)SU(2,1) and the Fourier Expansion of Automorphic Forms

The Generalized Whittaker Functions for $SU(2,1)$ and the Fourier Expansion of Automorphic Forms