Discrete Series Whittaker Functions on $Spin(2n,2)$

J. Math. Sci. Univ. Tokyo
Vol. 21 (2014), No. 1, Page 1–59.

Taniguchi, Kenji
Discrete Series Whittaker Functions on $Spin(2n,2)$
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Discrete series Whittaker functions on $Spin(2n, 2)$ are studied. The main results are the dimensions of Whittaker models and the explicit formulas of Whittaker functions. The dimensions of the spaces of algebraic and continuous Whittaker models are described by sums of dimensions of irreducible representations of $Spin(2n-3)$. As for the explicit formulas, we obtain Mellin-Barnes type integral representations for the Whittaker functions associated with minimal $K$-type vectors.

Keywords: Whittaker model, Invariants of representations, Confluent hypergeometric function, Mellin-Barnes integral representation.

Mathematics Subject Classification (2010): Primary 22E30; Secondary 22E46, 33C15, 11F30.
Mathematical Reviews Number: MR3235549

Received: 2009-06-08