
Journal of Lie Theory 25 (2015), No. 1, 271306 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 9928510, Japan hayata@yz.yamagatau.ac.jp Harutaka Koseki Dept. of Mathematics, Faculty of Education, Mie University, 1577 Kurimamachiyacho, Tsushi 5148507, Japan hkoseki@edu.mieu.ac.jp Tadashi Miyazaki Dept. of Mathematics, College of Liberal Arts and Sciences, Kitasato University, 1151 Kitasato / Minamiku, Sagamihara / Kanagawa, 2520373 Japan miyaza@kitasatou.ac.jp Takayuki Oda Graduate School of Mathematical Sciences, University of Tokyo, 381 Komaba, Meguroku / Tokyo, 1538914 Japan takayuki@ms.utokyo.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 nonholomorphic harmonic L^{2}sections in an SU(3,1)equivariant vector bundle. Keywords: Matrix coefficients, discrete series. MSC: 22E30, 22E45, 43A90 [ Fulltextpdf (430 KB)] for subscribers only. 