Lattices in semisimple groups and distal geometric structures.
Layer potentials C*-algebras of domains with conical points
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm...
Le corps des normes de certaines extensions infinies de corps locaux; applications
Le groupe de Poincaré et ses représentations
Le groupe de Poincaré et ses représentations. II. (algèbre de Lie, algèbre enveloppante)
Le problème d'équivalence pour les pseudogroupes de Lie : méthodes intrinsèques
Le spectre résiduel de
Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs.
Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. II
Lefschetz coincidence numbers of solvmanifolds with Mostow conditions
For any two continuous maps , between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of , . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.
Lefschetz numbers and twisted stabilized orbital integrals.
Left and right on locally compact groups.
Let G be a locally compact, non-compact group and f a function defined on G; we prove that, if f is uniformly continuous with respect to the left (right) structure on G and with a power integrable with respect to the left (right) Haar measure on G, then f must vanish at infinity. We prove that left and right cannot be mixed.
Left cells and domino tableaux in classical Weyl groups
Left thickness, left amenability and extreme left amenability.
Left-invariant almost complex structures and the associated metrics on four-dimensional direct products of Lie groups.
Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups
Left-symmetric algebras, or pre-Lie algebras in geometry and physics
In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs...
Leibniz's rule on two-step nilpotent Lie groups
Let be a nilpotent Lie algebra which is also regarded as a homogeneous Lie group with the Campbell-Hausdorff multiplication. This allows us to define a generalized multiplication of two functions in the Schwartz class (*), where and are the Abelian Fourier transforms on the Lie algebra and on the dual * and ∗ is the convolution on the group . In the operator analysis on nilpotent Lie groups an important notion is the one of symbolic calculus which can be viewed as a higher order generalization...
Lemme fondamental et endoscopie, une approche géométrique
Le “principe de fonctorialité”, conjecturé par Langlands à la fin des années 60, est un moyen remarquablement synthétique d’unifier et exprimer certains liens profonds entre formes automorphes, arithmétique et géométrie algébrique. Son apparente simplicité contraste fortement avec la difficulté des techniques utilisées pour l’aborder. Parmi celles-ci, la stabilisation de la formule des traces d’Arthur–Selberg bute depuis 25 ans sur une conjecture d’analyse harmonique sur des groupes -adiques :...
Lengths on semigroups and groups.