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We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .
Given an irreducible representation of a complex simply connected semisimple algebraic group we consider the closure of the image of in . We determine for which the variety is normal and for which is smooth.
On classifie les orbites de sur l’immeuble de Bruhat-Tits de pour trois paires sphériques de groupes -adiques classiques.
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