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Satake diagrams, Iwasawa decompositions, and representations of the exceptional Lie group \(F_ 4(-20)\). (English) Zbl 0571.22022

The parabolic subgroups of the noncompact, exceptional Lie group \(F_ 4(-20)\) are computed from a systematic analysis of Iwasawa and Langlands decompositions. Satake diagrams have been used to determine the involutive automorphisms of \(F_ 4(-20)\) which facilitate the Iwasawa decompositions. The polarizations associated with noncompact orbits with parabolic subgroups are computed. The represetations so obtained for these polarizations using Kostant’s induction scheme yield the principal series representations of \(F_ 4(-20)\)

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
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[1] DOI: 10.1007/BF01389744 · Zbl 0233.22005 · doi:10.1007/BF01389744
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