Journal of Lie Theory

no. 1
Matrix Coefficients of Discrete Series Representations of SU(3,1)
Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 271-306
For large discrete series representations of SU(3,1), we give expressions of the radial parts of their matrix coefficients in terms of the generalized hypergeometric series, and describe their asymptotic behavior, explicitly. Geometrically speaking, this is to obtain an explicit formula for some Hilbert space of non-holomorphic harmonic L2-sections in an SU(3,1)-equivariant vector bundle.
DOI: 10.5802/jolt.837
Classification: 22E30, 22E45, 43A90
Keywords: Matrix coefficients, discrete series 
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     author = {T. Hayata and H. Koseki and T. Miyazaki and T. Oda},
     title = {Matrix {Coefficients} of {Discrete} {Series} {Representations} of {SU(3,1)}},
     journal = {Journal of Lie Theory},
     pages = {271--306},
     year = {2015},
     volume = {25},
     number = {1},
     doi = {10.5802/jolt.837},
     zbl = {1316.22008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.837/}
}
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T. Hayata; H. Koseki; T. Miyazaki; T. Oda. Matrix Coefficients of Discrete Series Representations of SU(3,1). Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 271-306. doi: 10.5802/jolt.837

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