## Composition series and intertwining operators for the spherical principal series. II

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- by Kenneth D. Johnson
- Trans. Amer. Math. Soc.
**215**(1976), 269-283 - DOI: https://doi.org/10.1090/S0002-9947-1976-0385012-X
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## Abstract:

In this paper, we consider the connected split rank one Lie group of real type ${F_4}$ which we denote by $F_4^1$. We first exhibit $F_4^1$ as a group of operators on the complexification of A. A. Albertâs exceptional simple Jordan algebra. This enables us to explicitly realize the symmetric space $F_4^1/{\text {Spin}}(9)$ as the unit ball in ${{\mathbf {R}}^{16}}$ with boundary ${S^{15}}$. After decomposing the space of spherical harmonics under the action of ${\text {Spin}}(9)$, we obtain the matrix of a transvection operator of $F_4^1{\text {/Spin}}(9)$ 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 $F_4^1$.## References

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*Composition series and intertwining operators for the spherical principal series*. I (to appear).

## Bibliographic Information

- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**215**(1976), 269-283 - MSC: Primary 22E45; Secondary 43A80
- DOI: https://doi.org/10.1090/S0002-9947-1976-0385012-X
- MathSciNet review: 0385012