Tetraplectic structures, tri-momentum maps, and quaternionic flag manifolds

Details Tetraplectic structures, tri-momentum maps, and quaternionic flag manifolds Tetraplectic structures, tri-momentum maps, and quaternionic flag manifolds

2001-03-06

arxiv.org/abs/math/0103042v3

Mathematics

Differential Geometry

16 pages, enhanced and corrected

Scientific paper

10.1016/S0393-0440(01)00068-7

The purpose of this note is to define tri-moment maps for certain manifolds that carry closed non-degenerate 4-forms and an $Sp(1)^n$-action. Examples include quaternionic vector spaces and flag manifolds. We show how this map can be used ro reduce such manifolds to the ones with fewer symmetries. The images of such maps for quaternionic flag manifolds, which are defined using the Dieudonn\'e determinant, resemble the polytopes from the complex case.

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