Lifting smooth homotopies of orbit spaces
Linear actions of free groups
In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.
Linear free divisors and the global logarithmic comparison theorem
A complex hypersurface in is a linear free divisor (LFD) if its module of logarithmic vector fields has a global basis of linear vector fields. We classify all LFDs for at most .By analogy with Grothendieck’s comparison theorem, we say that the global logarithmic comparison theorem (GLCT) holds for if the complex of global logarithmic differential forms computes the complex cohomology of . We develop a general criterion for the GLCT for LFDs and prove that it is fulfilled whenever the...
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.
Manin’s and Peyre’s conjectures on rational points and adelic mixing
Let be the wonderful compactification of a connected adjoint semisimple group defined over a number field . We prove Manin’s conjecture on the asymptotic (as ) of the number of -rational points of of height less than , and give an explicit construction of a measure on , generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points on . Our approach is based on the mixing property of which we obtain with a rate of convergence.
Matrix entries of real representations of the groups and .
Matrix semigroups?generators and relations.
Maximal indexes of Tits algebras.
Maximal open compact subgroups of the projective symplectic group over a locally compact discrete valuation field
Maximal Subgroups of the Finite Orthogonal and Unitary Groups Stabilizing Anisotropic Subspaces.
McKay numbers and heights of characters.
Metaplectic covers of and the Gauss-Schering lemma
The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a -cocycle corresponding to a higher metaplectic extension of GL for any global field . In the case that has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity...