Non-trivial representations of the special relativitiy group.
Nouvelles approches de la propriété (T) de Kazhdan
Un groupe localement compact a la propriété (T) de Kazhdan si la -cohomologie de tout -module hilbertien est nulle. Cette propriété de rigidité de la théorie des représentations de a trouvé des applications qui vont de la théorie ergodique à la théorie des graphes. Pendant près de 30 ans, les seuls exemples connus de groupes avec la propriété (T), provenaient des groupes algébriques simples sur les corps locaux, ou de leurs réseaux. La situation a radicalement changé ces dernières années :...
On a variant of Kazhdan's property (T) for subgroups of semisimple groups
Let be an irreducible lattice in a product of simple groups. Assume that has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of in terms of the topology of the dual space of .We use this result to give a new proof for the triviality of the first cohomology group of with coefficients in a finite dimensional unitary representation.
On continuity of measurable group representations and homomorphisms
Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space ℒ(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to ℒ(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.
On Discrete Frames Associated with Semidirect Products.
On generalized d'Alembert functional equation.
Let G be a locally compact group. Let σ be a continuous involution of G and let μ be a complex bounded measure. In this paper we study the generalized d'Alembert functional equationD(μ) ∫G f(xty)dμ(t) + ∫G f(xtσ(y))dμ(t) = 2f(x)f(y) x, y ∈ G;where f: G → C to be determined is a measurable and essentially bounded function.
On infinitely small orbits
On invariant subalgebras of the Fourier-Stieltjes algebra of a locally compact group.
On Isolated Points in the Dual Spaces of Locally Compact Groups.
On Kazhdan's property (T) and Kazhdan constants associated to a Laplacian for SL(3,R).
On Kazhdan's property (T) for Sp(k).
On the Conjugation Representation of a Locally Compact Group.
On the Dual Object of a Compact Connected Group.
On the Existence of Pathological Submeasures and the Construction of Exotic Topological Groups.
On the primitive ideal space of a finitely generated nilpotent group.
On the Property P... of Locally Compact Groups
On the support of the conjugation representation for solvable locally compact groups.
On Weyl's reciprocity between group algebras and their commutants
Operator-Valued Positive Definite Kernels on Tubes.
Polarization and Unitary Representations of Solvable Lie Groups.