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)
School of Sciences, Harbin Inst. of Technology, Shenzhen, 518055, P. R. of China
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
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