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Journal of Lie Theory 23 (2013), No. 1, 085--112
Copyright Heldermann Verlag 2013

Whittaker Functions on Orthogonal Groups of Odd Degree

Taku Ishii
Faculty of Science and Technology, Seikei University, 3-3-1 Kichijoji-Kitamachi, Musashino, Tokyo 180-8633, Japan


\def\R{{\Bbb R}} We give explicit formulas for Whittaker functions for the class one principal series representations of the orthogonal groups SO$_{2n+1}(\R)$ of odd degree. Our formulas are similar to the recursive formulas for Whittaker functions on SL$_n(\R)$ given by Stade and the author.

Keywords: Whittaker functions, principal series representations.

MSC: 22E30, 33C80

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