Tuesday, December 9Misha Ershov, University of Virginia
I will talk about recent joint work with Andrei Jaikin-Zapirain where we prove that for any finitely generated (associative) ring R and any integer n≥3 the elementary linear group ELn(R) has property (T).
The majority of previous papers on property (T) for elementary linear groups over rings were based on the bounded generation method introduced by Shalom about 10 years ago. Using a recent generalization of that method, also due to Shalom, Vaserstein proved that the group ELn(R), n≥3, has property (T) when R is commutative—this generalized earlier results by Kassabov and Nikolov and by Shalom.
Like aforementioned works, our proof uses results of Shalom and Kassabov on relative property (T), but makes virtually no use of bounded generation. Instead we establish a new spectral ctirerion for property (T)—it is based on the notion of codistance between a finite family of subgroups of a group which generalizes the notion of epsilon-orthogonality introduced in the 2002 paper by Dymara and Januszkiewicz "Cohomology of buildings and their automorphism groups".Back to seminar home page.