Extension of Whittaker functions and test vectors
Representation Theory
2018-07-09 v3 Number Theory
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 -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.
Keywords
Cite
@article{arxiv.1710.04697,
title = {Extension of Whittaker functions and test vectors},
author = {Robert Kurinczuk and Nadir Matringe},
journal= {arXiv preprint arXiv:1710.04697},
year = {2018}
}
Comments
Previous title: Derivatives of representations of Whittaker type and test vectors. Final version to appear in Res. Number Theory