Quantitative Representation Stability Over Linear Groups
نویسندگان
چکیده
منابع مشابه
Representation stability and finite linear groups
We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include a proof of the Lannes– Schwartz Artinian conjecture in the generic representation theory of finite fields, very general homological stability theorems with t...
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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 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...
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In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra A. We give a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations, and a proof of the irreducibility of the tempered parabolic ...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2018
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rny250