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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 55 NO.1 / (2003))
Whittaker-Shintani Functions for Orthogonal Groups
Shin-Ichi Kato, Astushi Murase, Takashi Sugano,
Pages. 1-64
Abstract As generalization of zonal spherical functions and Whittaker functions,
certain special functions on $p$-adic orthogonal groups closely related to automorphic forms
are introduced. Their multiplicity one property and explicit formulae are established.
Contents Introduction
1. Unramified principal series representations
2. Equivalent linear forms
3. Orthogonal groups
4. Whittaker-Shintani functions
5. Cartan-type decompositions
6. Support of Whittaker-Shintani functions
7. Multiplicity one
8. Rank 1 calculation
9. Rationality
10. An explicit formula
11. The value at the identity : Proof of 10.8
Key words Spherical function, Whittaker function, orthogonal group, unramified principle series representation
Mathmatical Subject Classification 22E50, 11F70, 20G25, 22E35