The stabilizer subgroups of the automorphism group of certain real exceptional Jordan algebra

Details The stabilizer subgroups of the automorphism group of certain real exceptional Jordan algebra The stabilizer subgroups of the automorphism group of certain real exceptional Jordan algebra

2011-09-05

arxiv.org/abs/1109.0975v2

Mathematics

Differential Geometry

V2, 65 pages, presentation improved and minor errors corrected

Scientific paper

Let $\mathcal{J}^1$ be the real form of complex simple Jordan algebra with the automorphism group $F_{4(-20)}$. The stabilizer groups of $F_{4(-20)}$-orbit on $\mathcal{J}^1$ are determined. As an application, for $F_{4(-20)}$, the Bruhat and Gauss decomposition, the Iwasawa decomposition and also the Iwasawa decomposition with respect to $K_{\epsilon}$ in the sense of T. Oshima and J. Sekiguchi are given concretely.

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