|
Journal of Lie Theory 29 (2019), No. 3, 601--610 Copyright Heldermann Verlag 2019 Positivity of Principal Matrix Coefficients of Principal Series Representations of GLn(R) Yangyang Chen School of Sciences, Harbin Inst. of Technology, Shenzhen, 518055, P. R. of China chenyangyang@hit.edu.cn Let G = GLn(R), with the usual Cartan decomposition G = K exp(p0) and the usual Iwasawa decomposition G = NAK. We determine the image of exp(p0) 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 [ Fulltext-pdf (126 KB)] for subscribers only. |