منابع مشابه
Characteristic Classes and Representations of Discrete Subgroups of Lie Groups
A volume invariant is used to characterize those representations of a countable group into a connected semisimple Lie group G which are injective and whose image is a discrete cocompact subgroup of G. Let IT be a discrete cocompact subgroup of G and consider the analytic variety Hom(7r, G) consisting of homomorphisms 0: TT —> G. Denote by K a maximal compact subgroup of G and X = K\G the associ...
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Let K be a locally compact field and G a simple AT-group, G = G(K). A discrete subgroup T of G is called a lattice if G/F carries a finite G-invariant measure. It is a uniform (or cocompact) lattice if G/T is compact and nonuniform otherwise. When the jRf-rank of G is greater than one, Margulis [Ma, Z] proved that T is arithmetic, establishing the conjecture of Selberg and PiatetskiShapiro. Thi...
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A description of the Poisson boundary of random walks on discrete subgroups of semi-simple Lie groups in terms of geometric boundaries of the corresponding Riemannian symmetric spaces is given. Let G be a discrete group, and { a probability measure on G. A function f on G is called-harmonic if f(g) = P f(gx) (x) 8 g 2 G. The Poisson boundary of the pair (G;) is the probability space (?;) with a...
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Let Γ be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of Γ is nonpositive.
متن کاملCocompact Subgroups of Semisimple Lie Groups
Lattices and parabolic subgroups are the obvious examples of cocompact subgroups of a connected, semisimple Lie group with finite center. We use an argument of C. C. Moore to show that every cocompact subgroup is, roughly speaking, a combination of these. We study a cocompact subgroup H of a connected, semisimple Lie group G with finite center. The case where H is discrete is very important and...
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ژورنال
عنوان ژورنال: Topology
سال: 1970
ISSN: 0040-9383
DOI: 10.1016/0040-9383(70)90034-0