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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

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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