منابع مشابه
Representation Growth of Linear Groups
Let Γ be a group and rn(Γ) the number of its n-dimensional irreducible complex representations. We define and study the associated representation zeta function ZΓ(s) = ∞ ∑ n=1 rn(Γ)n . When Γ is an arithmetic group satisfying the congruence subgroup property then ZΓ(s) has an “Euler factorization”. The “factor at infinity” is sometimes called the “Witten zeta function” counting the rational rep...
متن کاملThe Growth of Linear Groups
Let G be a group generated by a finite subset S; define S to be the set Ž . < n < of all products of at most n elements of S, and let a S s S be the n n Ž . Ž . Ž . Ž . number of elements in S . As a S satisfies 1 F a S F a S ? a S , n nqm n m Ž .1r n Ž . Ž .1r n the limit lim a S exists, and a S s lim a S G 1. Although the n n Ž . exact value of a S depends on the generating set S, it is well ...
متن کاملRepresentation Growth for Linear Groups
Let Γ be a group and rn(Γ) the number of its n-dimensional irreducible complex representations. We define and study the associated representation zeta function ZΓ(s) = ∞ ∑ n=1 rn(Γ)n . When Γ is an arithmetic group satisfying the congruence subgroup property then ZΓ(s) has an “Euler factorization”. The “factor at infinity” is sometimes called the “Witten zeta function” counting the rational rep...
متن کاملBoundaries of systolic groups
For all systolic groups we construct boundaries which are EZ–structures. This implies the Novikov conjecture for torsion–free systolic groups. The boundary is constructed via a system of distinguished geodesics in a systolic complex, which we prove to have coarsely similar properties to geodesics in CAT (0) spaces. MSC: 20F65; 20F67; 20F69;
متن کاملEG for systolic groups
We prove that if a group G is systolic, i.e. if it acts properly and cocompactly on a systolic complex X, then an appropriate Rips complex constructed from X is a finite model for EG.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc12747