Journal of Lie Theory 25 (2015), No. 1, 271--306
Copyright Heldermann Verlag 2015
Matrix Coefficients of Discrete Series Representations of SU(3,1)
Takahiro Hayata
Dept. of Applied Mathematics and Physics, Graduate School of Science and Engineering, Yamagata University, Yonezawa 992-8510, Japan
hayata@yz.yamagata-u.ac.jp
Harutaka Koseki
Dept. of Mathematics, Faculty of Education, Mie University, 1577 Kurimamachiya-cho, Tsushi 514-8507, Japan
h-koseki@edu.mie-u.ac.jp
Tadashi Miyazaki
Dept. of Mathematics, College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato / Minamiku, Sagamihara / Kanagawa, 252-0373 Japan
miyaza@kitasato-u.ac.jp
Takayuki Oda
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguroku / Tokyo, 153-8914 Japan
takayuki@ms.u-tokyo.ac.jp
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.
Keywords: Matrix coefficients, discrete series.
MSC: 22E30, 22E45, 43A90
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