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Rigidity of proper almost-homogeneous domains in positive flag manifolds

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arxiv 2407.18747 v2 pith:VAVL456D submitted 2024-07-26 math.GR math.DGmath.GTmath.MG

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classification math.GRmath.DGmath.GTmath.MG
keywords manifoldspositiveproperboundaryflagrigidityshilovadmitting
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abstract

We show that, inside the Shilov boundary of any given Hermitian symmetric space of tube type, there is, up to isomorphism, only one proper domain such that every point on its boundary belongs to the closure of an orbit under its automorphism group. This gives a classification of all closed proper manifolds locally modelled on such Shilov boundaries, and provides a positive answer, in the case of flag manifolds admitting a $\Theta$-positive structure, to a rigidity question of Limbeek and Zimmer.

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  1. Transverse groups preserving proper domains in flag manifolds

    math.RT 2025-07 reject novelty 8.0 of 10

    Transverse groups preserving proper domains in flag manifolds must have limit triples of a single type (Maslov index zero in the tube-type case), but the proof of this key claim contains a false step.

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