Existence of compact quotients of homogeneous spaces, measurably proper actions, and decay of matrix coefficients
Existence of generalized symmetric Riemannian spaces with solvable isometry group
Existence of infinite-dimensional Lie algebra for a unitary group on a Hilbert space and related aspects
We show that for any strongly closed subgroup of a unitary group of a finite von Neumann algebra, there exists a canonical Lie algebra which is complete with respect to the strong resolvent topology. Our analysis is based on the comparison between measure topology induced by the tracial state and the strong resolvent topology we define on the particular space of closed operators on the Hilbert space. This is an expository article of the paper by both authors in Hokkaido Math. J. 41 (2012), 31-99,...
Existence of solutions for transversally elliptic left invariant differential operators on nilpotent Lie groups
Explicit description of a family of affine Kac-Moody groups. (Description explicite d'une famille de groupes de Kac-Moody affines.)
Explicit geodesic flow-invariant distributions using -representation ladders.
Explicit Hilbert spaces for certain unipotent representations.
Explicit Howe duality in the stable range.
Explicit Kazhdan constants for representations of semisimple and arithmetic groups
Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property . For any such group, , we present a Kazhdan set of two elements, and compute its best Kazhdan constant. Then, settling a question raised by Serre and by de la Harpe and Valette, explicit Kazhdan constants for every lattice in are obtained, for a “geometric” generating set of the form , where is a ball of radius , and the dependence of on is described explicitly....
Exponential functionals of brownian motion and class-one Whittaker functions
We consider exponential functionals of a brownian motion with drift in ℝn, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on the law of...
Exponential Lie groups with disconnected near Cartan subgroups.
Exponential mapping for Lie groupoids. Applications
Exponents in Archimedean Arthur packets
Generalizing the proof – by Hecht and Schmid – of Osborne’s conjecture we prove an Archimedean (and weaker) version of a theorem of Colette Moeglin. The result we obtain is a precise Archimedean version of the general principle – stated by the second author – according to which a local Arthur packet contains the corresponding local -packet and representations which are more tempered.
Expression for a general element of an matrix.
Extension of the Poincaré symmetry and its field theoretical implementation.
Extension of Wang-Gong monotonicity result in semisimple Lie groups
We extend a monotonicity result of Wang and Gong on the product of positive definite matrices in the context of semisimple Lie groups. A similar result on singular values is also obtained.
Extensions Between Generalized Verma Modules: The Hermitian Symmetric Cases.
Extensions de Lie et groupes d'automorphismes de corps locaux
Extensions de représentations induites des produits semi-directs.
Extensions des représentations des groupes de Lie construites par M. Duflo.