Method of replacing the variables for generalized symmetry of the D'Alembert equation.
Monogenic functions in conformal geometry.
Nonclassical approximate symmetries of evolution equations with a small parameter.
Nonlocal symmetries and generation of solutions for partial differential equations.
On a new normalization for tractor covariant derivatives
A regular normal parabolic geometry of type on a manifold gives rise to sequences of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative on the corresponding tractor bundle , where is the normal Cartan connection. The first operator in the sequence is overdetermined and it is well known that yields the prolongation of this operator in the homogeneous case . Our first main result...
On formal theory of differential equations. I.
On the composition structure of the twisted Verma modules for
We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra , including the explicit structure of singular vectors for both and one of its Lie subalgebras , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as -modules on the Schubert cells in the full flag manifold for .
On the Laplace-Beltrami operator on the oscillator group.
On the order of natural differential operators and liftings
Opérateurs elliptiques et mesures sur l'espace des lacets invariants par le groupe des difféomorphismes du cercle
Persistence of invariant manifolds for perturbations of semiflows with symmetry.
Projective connections, double fibrations and formal neighbourhoods of lines.
Representations of groups on eigenspaces of invariant differential operators
Résolubilité sur un espace riemannien symétrique
Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators
We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in norm, at Lebesgue points and almost everywhere. We also prove localization results.
Rochlin invariants, theta functions and the holonomy of some determinant line bundles.
Scalar differential invariants of symplectic Monge-Ampère equations
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential invariants...
Singularity analysis and integrability of a Burgers-type system of Foursov.
Solvable nonlinear evolution PDEs in multidimensional space.
Some curvature identities for commutative spaces