Naive boundary strata and nilpotent orbits

Kerr, Matt; Pearlstein, Gregory

doi:10.5802/aif.2923

Naive boundary strata and nilpotent orbits
[Limites de strates naïves et orbites nilpotentes]

Kerr, Matt ¹ ; Pearlstein, Gregory ²

¹ Department of Mathematics, Campus Box 1146 Washington University in St. Louis St. Louis, MO 63130 (USA)
² Mathematics Department, Mail stop 3368 Texas A&M University College Station, TX 77843 (USA)

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

Résumé
Abstract

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 $S U (2, 1)$ , $S p_{4}$ , 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 $S U (2, 1)$ , $S p_{4}$ , and $G_{2}$ .

MR Zbl

DOI : 10.5802/aif.2923

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

Affiliations des auteurs :

Kerr, Matt ¹ ; Pearlstein, Gregory ²

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     title = {Naive boundary strata and nilpotent orbits},
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Kerr, Matt; Pearlstein, Gregory. Naive boundary strata and nilpotent orbits. Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2659-2714. doi : 10.5802/aif.2923. https://aif.centre-mersenne.org/articles/10.5802/aif.2923/

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