A Remark on Discontinuous Translation Invariant Functionals on L... (G) for Certain Compact Groups G.
A Remark on Invariant Pseudo-Differential Operators.
A remark on my paper "On the Saito-Kurokawa lifting".
A remarkable contraction of semisimple Lie algebras
Recently, E.Feigin introduced a very interesting contraction of a semisimple Lie algebra (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of . For instance, the algebras of invariants of both adjoint and coadjoint representations of are free, and also the enveloping algebra of is a free module over its centre.
A representation independent propagator I : compact Lie groups
A representation independent propagator. II : Lie groups with square integrable representations
A restriction theorem for the Heisenberg motion
We prove a restriction theorem for the class-1 representations of the Heisenberg motion group. This is done using an improvement of the restriction theorem for the special Hermite projection operators proved in [13]. We also prove a restriction theorem for the Heisenberg group.
A reverse engineering approach to the Weil representation
We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.
A rigidity phenomenon for germs of actions of
We study germs of Lie algebras generated by two commuting vector fields in manifolds that are maximal in the sense of Palais (those which do not present any evident obstruction to be the local model of an action of ). We study three particular pairs of homogeneous quadratic commuting vector fields (in , and ) and study the maximal Lie algebras generated by commuting vector fields whose 2-jets at the origin are the given homogeneous ones. In the first case we prove that the quadratic algebra...
A rigidity theorem for Möbius groups.
A saturation property for powers of irreducible characters.
A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus.
A semi-group of probability measures with non-smooth differentiable densities on a Lie group
A separately, but not jointly continuous action of a compact semilattice.
A Series of Unitary Irreducible Representations Induced from a Symmetric Subgroup of a Semisimple Lie Group.
A Short Proof of a Classical Covering Lemma.
A short proof of ß(G.. {1}) = G for non-metrizable compact groups.
A short proof of the Campbell-Hausdorff formula. (Une courte démonstration de la formule de Campbell-Hausdorff.)
A simple characterization of sets satisfying the central sets theorem.
A Simple Proof of Borel's Density Theorem.