Property (T) for Kac-Moody groups over rings
Group Theory
2017-08-08 v1 Representation Theory
Abstract
Let R be a finitely generated commutative ring with 1, let A be an indecomposable 2-spherical generalized Cartan matrix of size at least 2 and M=M(A) the largest absolute value of a non-diagonal entry of A. We prove that there exists an integer n=n(A) such that the Kac-Moody group G_A(R) has property (T) whenever R has no proper ideals of index less than n and all positive integers less than or equal to M are invertible in R.
Cite
@article{arxiv.1708.01968,
title = {Property (T) for Kac-Moody groups over rings},
author = {Mikhail Ershov and Ashley Rall and Zezhou Zhang},
journal= {arXiv preprint arXiv:1708.01968},
year = {2017}
}
Comments
24 pages. This is an extended version of the paper with the same title by the first two authors (to appear in the Journal of Algebra) with an appendix by the third author