Linear Groups of Finite Cohomological Dimension.
Linear groups with large cyclic subgroups and translation planes
Linear maps preserving orbits
Let be a connected complex reductive group where is a finite-dimensional complex vector space. Let and let . Following Raïs we say that the orbit is characteristic for if the identity component of is . If is semisimple, we say that is semi-characteristic for if the identity component of is an extension of by a torus. We classify the -orbits which are not (semi)-characteristic in many cases.
Linear models for reductive group actions on affine quadrics
Linear preserver problems and algebraic groups.
Linearizing some actions on affine space
Local-global principle for congruence subgroups of Chevalley groups
Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and...
Longest Weight Vectors and Excellent Filtrations.
Lusztig conjectures, old and new, I.