Geodesic
Matrix Coefficients of Discrete Series Representations of SU(3,1)
Takahiro Hayata1 ; Harutaka Koseki2 ; Tadashi Miyazaki3 ; Takayuki Oda4
1Dept. of Applied Mathematics and Physics, Graduate School of Science and Engineering, Yamagata University, Yonezawa 992-8510, Japan
2Dept. of Mathematics, Faculty of Education, Mie University, 1577 Kurimamachiya-cho, Tsushi 514-8507, Japan
3Dept. of Mathematics, College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato / Minamiku, Sagamihara / Kanagawa, 252-0373 Japan
4Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguroku / Tokyo, 153-8914 Japan
Journal of Lie Theory, Tome 25 (2015) no. 1, pp. 271-306

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22E30, 22E45, 43A90
Mots-clés : Matrix coefficients, discrete series

Takahiro Hayata  1   ; Harutaka Koseki  2   ; Tadashi Miyazaki  3   ; Takayuki Oda  4

1 Dept. of Applied Mathematics and Physics, Graduate School of Science and Engineering, Yamagata University, Yonezawa 992-8510, Japan
2 Dept. of Mathematics, Faculty of Education, Mie University, 1577 Kurimamachiya-cho, Tsushi 514-8507, Japan
3 Dept. of Mathematics, College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato / Minamiku, Sagamihara / Kanagawa, 252-0373 Japan
4 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguroku / Tokyo, 153-8914 Japan 
Takahiro Hayata; Harutaka Koseki; Tadashi Miyazaki; Takayuki Oda. Matrix Coefficients of Discrete Series Representations of SU(3,1). Journal of Lie Theory, Tome 25 (2015) no. 1, pp. 271-306. http://geodesic.mathdoc.fr/item/JOLT_2015_25_1_a13/
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     title = {Matrix {Coefficients} of {Discrete} {Series} {Representations} of {SU(3,1)}},
     journal = {Journal of Lie Theory},
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     year = {2015},
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