On Invariant Differential Forms on Group Varieties

Automorphic Forms on Shimura Varieties

Characteristic Varieties and Logarithmic Differential 1-forms

We introduce in this paper a hypercohomology version of the resonance varieties and obtain some relations to the characteristic varieties of rank one local systems on a smooth quasi-projective complex variety M , see Theorem (3.1) and Corollaries (3.2) and (4.2). A logarithmic resonance variety is also considered in Proposition (4.5). As an application, we determine the first characteristic var...

Invariant Differential Operators On

For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...

Tracking Invariant Manifolds without Differential Forms

A frequently studied problem of geometric singular perturbation theory consists in establishing the presence of trajectories of certain types (homoclinic, heteroclinic, satisfying given boundary conditions, etc.) approximating singular ones for the unperturbed problem. A useful tool for this problem has been established in Jones et al. [2] and called “Exchange Lemma” by the authors. It resemble...

Differential Operators on Grassmann Varieties

Following Weyl’s account in The Classical Groups we develop an analogue of the (first and second) Fundamental Theorems of Invariant Theory for rings of differential operators: when V is a k-dimensional complex vector space with the standard SLkC action, we give a presentation of the ring of invariant differential operators D(C[V n])SLkC and a description of the ring of differential operators on...