Universal lattices and unbounded rank expanders

• 成果类型: Article
• 署名作者: Kassabov, Martin
• 署名单位: Cornell University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0064-z
• 发表日期: 2007
• 页码: 297-326
• 关键词: kazhdan constants

摘要

We study the representations of non- commutative universal lattices and use them to compute lower bounds of the tau- constant for the commutative universal lattices G(d),(k) = SLd( Z[ x(1),..., x(k)]), for d >= 3 with respect to several generating sets. As an application we show that the Cayley graphs of the finite groups SL3k( F-p) can be made expanders with a suitable choice of generators. This provides the first example of expander families of groups of Lie type, where the rank is not bounded and provides counter examples to two conjectures of A. Lubotzky and B. Weiss.