Book Review: Discrete subgroups of semisimple Lie groups
نویسندگان
چکیده
منابع مشابه
Cocompact 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...
متن کاملParabolic Subgroups of Semisimple Lie Groups and Einstein Solvmanifolds
In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci curvatures of our solvmanifolds coincide with the restrictions of the Ricci curvatures of the ambient symmetric spaces. Consequently, all of our solvmanifolds...
متن کاملHarish-chandra’s Schwartz Algebras Associated with Discrete Subgroups of Semisimple Lie Groups
We prove that the Harish-Chandra’s Schwartz space associated with a discrete subgroup of a semisimple Lie group is a dense subalgebra of the reduced C∗-algebra of the discrete subgroup. Then, we prove that the reduced C∗-norm is controlled by the norm of the Harish-Chandra’s Schwartz space. This inequality is weaker than property RD and holds for any discrete group acting isometrically, properl...
متن کاملRepresentations of Semisimple Lie Groups
Let G be a Lie group and § a Banach space. A representation n of G on § is a mapping which assigns to every element x in G a bounded linear operator n(x) on § such that the following two conditions are fulfilled: (1) 7t(xy) = n(x) 7i(y) (x, y e G),n(l) = / and (2) the mapping (x, tp) ->uz(x)y) of G x § into § is continuous. (Here 1 is the unit element of G and I is the unit operator,) In partic...
متن کاملRepresentations of Semisimple Lie Groups
Fifty years ago, at the International Congress in Bologna, Hermann Weyl gave a report on representations of compact groups and, in particular, of compact Lie groups. Most of the important results had just been proved by him and by others, and at the time of his lecture, in 1928, the representation theory of compact Lie groups had become a very appealing subject. To a large extent, Weyl's theory...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1992
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1992-00306-3