Composition Series and Intertwining Operators for the Spherical Principal Series
نویسندگان
چکیده
In this paper, we consider the connected split rank one Lie group of real type F4 which we denote by F4. We first exhibit F4 as a group of operators on the complexification of A. A. Albert's exceptional simple Jordan algebra. This enables us to explicitly realize the symmetric space F4/Spin(9) as the unit ball in R with boundary S . After decomposing the space of spherical harmonics under the action of Spin(9), we obtain the matrix of a transvection operator of F4/Spin(9) acting on a spherical principal series representation. We are then able to completely determine the Jordan Holder series of any spherical principal series representation of F4.
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