Journal of Lie Theory

no. 3
Positivity of Principal Matrix Coefficients of Principal Series Representations of GLn(R)
Journal of Lie Theory, Volume 29 (2019) no. 3, pp. 601-610
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.
DOI: 10.5802/jolt.1071
Classification: 22E45, 22E15
Keywords: General linear group, Iwasawa decomposition, matrix coefficient, principal series representation 
@article{JOLT_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--610},
     year = {2019},
     volume = {29},
     number = {3},
     doi = {10.5802/jolt.1071},
     zbl = {1425.22010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1071/}
}
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%A Y. Chen
%T Positivity of Principal Matrix Coefficients of Principal Series Representations of GLn(R)
%J Journal of Lie Theory
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Y. Chen. Positivity of Principal Matrix Coefficients of Principal Series Representations of GLn(R). Journal of Lie Theory, Volume 29 (2019) no. 3, pp. 601-610. doi: 10.5802/jolt.1071

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