Naive boundary strata and nilpotent orbits

Kerr, Matt; Pearlstein, Gregory

Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2659-2714.

Nous donnons une paramétrisation de certaines orbites de groupes de Lie réels dans le dual compact d’un domaine de Mumford-Tate et une caractérisation des orbites qui contiennent une filtration limite de Hodge naïve. Une série d’exemples est élaborée pour les groupes $SU(2,1)$, $S{p}_4$, et $G_2$.

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 $SU(2,1)$, $S{p}_4$, and $G_2$.

Classification : 14D07, 14M17, 17B45, 20G99, 32M10, 32G20
Keywords: Mumford-Tate groups, Mumford-Tate domains, nilpotent orbits, variation of Hodge structure, Shimura varieties
Mot clés : groupes de Mumford-Tate, domaine de Mumford-Tate, orbites nilpotentes, variation de structure de Hodge, variétés de Shimura

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