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 کاملon the effect of linear & non-linear texts on students comprehension and recalling
چکیده ندارد.
15 صفحه اولRegularities on the Cayley Graphs of Groups of Linear Growth
Let G be a finitely generated group and E 5 E 1 < E 2 1 a finite generating system . Define the E -length l E ( g ) of g P G as the minimum length of a representation of g as a product of elements in E , and define f E ( n ) as the number of elements in G with E -length equal to n . We will say that a finitely generated group has polynomial growth if there exists an integer k such that f E ( n ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2015
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm228-1-4