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arXiv · 1710.04697

Extension of Whittaker functions and test vectors

Robert Kurinczuk·Nadir Matringe
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Abstract

We show that certain products of Whittaker functions and Schwartz functions on a general linear group extend to Whittaker functions on a larger general linear group. This generalizes results of Cogdell--Piatetski-Shapiro \cite{CPS} and Jacquet--Piatetski-Shapiro--Shalika \cite{JPSS83}. As a consequence, we prove that the Rankin--Selberg $L$-factor of the product of a discrete series representation and the Zelevinsky dual of a discrete series representation is given by a single Rankin--Selberg integral.

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Robert Kurinczuk, Nadir Matringe. 2017-10-12. Extension of Whittaker functions and test vectors. https://arxiv.org/abs/1710.04697

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