Properties of nilpotent orbit complexification

2015/05/28 by Crooks, Peter
#06A07 #17B05 (secondary) #17B08 (primary) #20G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1505.07729

Abstract

We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra \mathfrakg and those in its complexification \mathfrakg_ℂ. In particular, we prove that two distinct real nilpotent orbits lying in the same complex orbit are incomparable in the closure order. Secondly, we characterize those \mathfrakg having non-empty intersections with all nilpotent orbits in \mathfrakg_ℂ. Finally, for \mathfrakg quasi-split, we characterize those complex nilpotent orbits containing real ones.

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