Geodesic
Positivity of Principal Matrix Coefficients of Principal Series Representations of GLn(R)
Journal of Lie theory, Tome 29 (2019) no. 3, pp. 601-61
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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.
Classification : 22E45, 22E15
Mots-clés : General linear group, Iwasawa decomposition, matrix coefficient, principal series representation 
@article{JLT_2019_29_3_JLT_2019_29_3_a0,
     author = {Y. Chen},
     title = {Positivity of {Principal} {Matrix} {Coefficients} of {Principal} {Series} {Representations} of {GL\protect\textsubscript{n}(R)}},
     journal = {Journal of Lie theory},
     pages = {601--61},
     year = {2019},
     volume = {29},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2019_29_3_JLT_2019_29_3_a0/}
}
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Y. Chen. Positivity of Principal Matrix Coefficients of Principal Series Representations of GLn(R). Journal of Lie theory, Tome 29 (2019) no. 3, pp. 601-61. http://geodesic.mathdoc.fr/item/JLT_2019_29_3_JLT_2019_29_3_a0/