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hal-00582700, version 3

## Hua operators, Poisson transform and relative discrete series on line bundle over bounded symmetric domains

Khalid Koufany () 1, Genkai Zhang 2

Journal of Functional Analysis 262, 9 (2012) 4140-4159

Abstract: Let $D=G/K$ be a bounded symmetric domain and $S=K/L$ be its Shilov boundary We consider the action of $G$ with weight $\nu\in\mathbb{Z}$ on functions on $D$ viewed as sections the line bundle and the corresponding eigenspace of $G$-invariant di erential operators. The Poisson transform maps hyperfunctions on the $S$ to the eigenspaces. We characterize the image in terms of Hua operators on the sections of the line bundle. For some special parameter the Poisson transform is of Szegö type mapping into the relative discrete series; we compute the corresponding elements in the discrete series.

• 1:  Institut Elie Cartan Nancy (IECN)
• CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
• 2:  Chalmers University of Technology
• Göteborg University
• Domain : Mathematics/Representation Theory
• Keywords : Hua operator – Poisson transform – Bounded symmetric domain – Homogeneous line bundle – Relative discrete series
• Available versions :  v1 (2011-04-04) v2 (2011-05-20) v3 (2011-05-30)

• hal-00582700, version 3
• oai:hal.archives-ouvertes.fr:hal-00582700
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• Submitted on: Friday, 27 May 2011 14:48:24
• Updated on: Monday, 25 June 2012 09:25:11