Let J1 be the real form of a complex simple Jordan algebra such
that the automorphism group is F4(−20). By using some orbit types
of F4(−20) on J1, for F4(−20),
explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's
Kϵ−Iwasawa decomposition, the Matsuki decomposition, and the Bruhat
and Gauss decompositions.Comment: v3, 30 pages, 1 figure, major changes from v2 by separating section
9--14, reformatted, and the title changed to appear in Tsukuba J. of Mat