2013/09/27 by Dave Witte Morris, Morris, Dave Witte, Kevin Wortman +1
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1309.7113
Suppose Gamma is an S-arithmetic subgroup of a connected, semisimple algebraic group G over a global field Q (of any characteristic). It is well known that Gamma acts by isometries on a certain CAT(0) metric space XS that is a Cartesian product of Euclidean buildings and Riemannian symmetric spaces. For a point p on the visual boundary of XS, we show there exists a horoball based at p that is disjoint from some Gamma-orbit in XS if and only if p lies on the boundary of a certain type of flat in XS that we call "Q-good." This generalizes a theorem of G.Avramidi and D.W.Morris that characterizes the horospherical limit points for the action of an arithmetic group on its associated symmetric space.