Symmetric subgroups of rational groups of hermitian type

Details Symmetric subgroups of rational groups of hermitian type Symmetric subgroups of rational groups of hermitian type

1995-05-29

arxiv.org/abs/alg-geom/9505033v1

Mathematics

Algebraic Geometry

29 pages (11 pt), ps-file also available at the home page http://www.mathematik.uni-kl.de/~wwwagag, preprints. LaTeX v2.09

Scientific paper

A rational group of hermitian type is an algebraic group over the rational numbers whose symmetric space is a hermitian symmetric space. We assume such a group $G$ to be given, which we assume is isotropic. Then, for any rational parabolic $P$ in the group $G$, we find a reductive rational subgroup $N$ closely related with $P$ by a relation we call incidence. This has implications to the geometry of arithmetic quotients of the symmetric space by arithmetic subgroups of $G$, in the sense that $N$ defines a subvariety on such an arithmetic quotient which has special behaviour at the cusp corresponding to the parabolic with which $N$ is incident.

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