
Journal of Lie Theory 29 (2019), No. 3, 601610 Copyright Heldermann Verlag 2019 Positivity of Principal Matrix Coefficients of Principal Series Representations of GL_{n}(R) Yangyang Chen School of Sciences, Harbin Inst. of Technology, Shenzhen, 518055, P. R. of China chenyangyang@hit.edu.cn Let G = GL_{n}(R), with the usual Cartan decomposition G = K exp(p_{0}) and the usual Iwasawa decomposition G = NAK. We determine the image of exp(p_{0}) under the projection of G to K through the Iwasawa decomposition. As an application, we prove a positivity result about the matrix coefficients of principal series representations of G. Keywords: General linear group, Iwasawa decomposition, matrix coefficient, principal series representation. MSC: 22E45, 22E15 [ Fulltextpdf (126 KB)] for subscribers only. 