Property (T) for Groups Graded by Root Systems

Download or read book Property (T) for Groups Graded by Root Systems written by Mikhail Ershov and published by . This book was released on 2017 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors introduce and study the class of groups graded by root systems. They prove that if \Phi is an irreducible classical root system of rank \geq 2 and G is a group graded by \Phi, then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of G. As the main application of this theorem the authors prove that for any reduced irreducible classical root system \Phi of rank \geq 2 and a finitely generated commutative ring R with 1, the Steinberg group {\mathrm St}_{\Phi}(R) and the elementary Chevalley group \mathbb E_{\Phi}(R) have property (T).