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Sieve methods in group theory I: Powers in Linear groups
Sieve Property-T Powers Linear groups Finite groups of Lie type
2011/9/14
Abstract: A general sieve method for groups is formulated. It enables one to "measure" subsets of a finitely generated group. As an application we show that if $\Gamma$ is a finitely generated non vir...
Homotopy invariance for homology of linear groups: reductions and the rank two case
linear groups the rank two case
2010/11/24
We discuss the problem of homotopy invariance for homology of linear groups. Some reductions we are able to make show that homotopy invariance for linear groups follows from contractibility of a cert...
A problem of Kollar and Larsen on finite linear groups and crepant resolutions
Age deviation finite linear groups complex reflection groups
2010/12/6
The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calab...
Hartley´s Theorem on Representations of the General Linear Groups and Classical Groups
subgroups of classical groups representation theory of algebraic groups
2010/2/26
We suggest a new proof of Hartley's theorem on representations of the general linear groups GLn(K) where K is a field. Let H be a subgroup of GLn(K) and E the natural GLn(K)-module. Suppose that the r...