New holomorphically closed subalgebras of C∗C^*-algebras of hyperbolic groups

We construct dense, unconditional subalgebras of the reduced group $C^*$-algebra of a word-hyperbolic group, which are closed under holomorphic functional calculus and possess many bounded traces. Applications to the cyclic cohomology of group $C^*$-algebras and to delocalized $L^2$-invariants of negatively curved manifolds are given

Algebraic and analytic Dirac induction for graded affine Hecke algebras

We define the algebraic Dirac induction map \Ind_D for graded affine Hecke algebras. The map \Ind_D is a Hecke algebra analog of the explicit realization of the Baum-Connes assembly map in the $K$-theory of the reduced $C^*$-algebra of a real reductive group using Dirac operators. The definition of \Ind_D is uniform over the parameter space of the graded affine Hecke algebra. We show that the map \Ind_D defines an isometric isomorphism from the space of elliptic characters of the Weyl group (relative to its reflection representation) to the space of elliptic characters of the graded affine Hecke algebra. We also study a related analytically defined global elliptic Dirac operator between unitary representations of the graded affine Hecke algebra which are realized in the spaces of sections of vector bundles associated to certain representations of the pin cover of the Weyl group. In this way we realize all irreducible discrete series modules of the Hecke algebra in the kernels (and indices) of such analytic Dirac operators. This can be viewed as a graded Hecke algebra analogue of the construction of discrete series representations for semisimple Lie groups due to Parthasarathy and Atiyah-Schmid.Comment: 37 pages, revised introduction, updated references, minor correction

Quantum Symmetries and Strong Haagerup Inequalities

In this paper, we consider families of operators $\{x_r\}_{r \in \Lambda}$ in a tracial C$^\ast$-probability space $(\mathcal A, \phi)$, whose joint $\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\{H_n^+\}_{n \in \N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\mathcal B$ generated by $\{x_r\}_{r \in \Lambda}$, which generalizes the strong Haagerup inequalities for $\ast$-free R-diagonal families obtained by Kemp-Speicher \cite{KeSp}. As an application of our result, we show that $\mathcal B$ always has the metric approximation property (MAP). We also apply our techniques to study the reduced C$^\ast$-algebra of the free unitary quantum group $U_n^+$. We show that the non-self-adjoint subalgebra $\mathcal B_n$ generated by the matrix elements of the fundamental corepresentation of $U_n^+$ has the MAP. Additionally, we prove a strong Haagerup inequality for $\mathcal B_n$, which improves on the estimates given by Vergnioux's property RD \cite{Ve}

Etude télécrânienne des mouvements cervicaux et palatins au cours de la croissance

The sagittal and anterior position of the hyoid bone is at the origin of the changes in orientation of the palatine laminae. A posterior-anterior movement of this bone allows the tongue to liberate the posterior part of the oral cavity; the palatine laminae rotate forwards and downwards. The opposite case is verified in the same way; the naso-palatine canal is a very malleable area, allowing a lowering of the anterior part of the palatine laminae. The vertical variations of the hyoid bone have little effect on the palate.La position sagittale de l’os hyoïde est à l’origine des modifications d’orientation des lames palatines. Ceci a été montré à partir de télécrânes sagittaux. Un mouvement postéro-antérieur de cet os permet à la langue de libérer la partie postérieure de la cavité buccale: les lames palatines font une rotation vers le bas et l’avant. Le contraire se vérifie de la même façon. Le canal naso-palatin est une zone très plastique; il permet un abaissement de la partie antérieure de la lame palatine. Les variations verticales hyoïdiennes influencent peu le palais

Uniformizing the Stacks of Abelian Sheaves

Elliptic sheaves (which are related to Drinfeld modules) were introduced by Drinfeld and further studied by Laumon--Rapoport--Stuhler and others. They can be viewed as function field analogues of elliptic curves and hence are objects "of dimension 1". Their higher dimensional generalisations are called abelian sheaves. In the analogy between function fields and number fields, abelian sheaves are counterparts of abelian varieties. In this article we study the moduli spaces of abelian sheaves and prove that they are algebraic stacks. We further transfer results of Cerednik--Drinfeld and Rapoport--Zink on the uniformization of Shimura varieties to the setting of abelian sheaves. Actually the analogy of the Cerednik--Drinfeld uniformization is nothing but the uniformization of the moduli schemes of Drinfeld modules by the Drinfeld upper half space. Our results generalise this uniformization. The proof closely follows the ideas of Rapoport--Zink. In particular, analogies of $p$-divisible groups play an important role. As a crucial intermediate step we prove that in a family of abelian sheaves with good reduction at infinity, the set of points where the abelian sheaf is uniformizable in the sense of Anderson, is formally closed.Comment: Final version, appears in "Number Fields and Function Fields - Two Parallel Worlds", Papers from the 4th Conference held on Texel Island, April 2004, edited by G. van der Geer, B. Moonen, R. Schoo

Influence du développement vertical du massif facial supérieur sur les différents composants palatins

We put the vertical rotations of the premaxilla and of the hard palate in relation with the vertical development of the maxillary fied. The latter has been evaluated by the changes of length of the right segment that was defined by the prof. Delaire point and its MH1 projection of the hard palate.The vertical variations of the maxillary fields, evaluated from the M-MH1, have an influence on the orientation of the hard palate and the premaxilla in relation to the angle of the pterygoclivian compass.This action is very perceptible at the level of the premaxilla-palatinal junction. It is lower at the level of the hard palate and of the premaxilla when these are separately studied.We got the impression that the front and the back nasal thorns are relatively steady zones during the growth compared to the premaxillo-palatinal junction.Nous avons mis en relation les rotations dans le sens vertical du prémaxillaire et des lames palatines avec le développement vertical du champ maxillaire. Celui-ci a été évalué par les changements de longueur du segment de droite défini par le point M. de DELAIRE et sa projection MH1 sur les lames palatines.Les variations verticales du champ maxillaire, évaluées à partir de MMH1 influencent l'orientation des lames palatines et du prémaxillaire par rapport au compas ptérygo-clivien. Cette action est fort sensible au niveau de la jonction prémaxillo-palatine. Elle est moindre au niveau des lames palatines et du prémaxillaire lorsque ceux-ci sont étudiés séparément.Nous avons tiré l'impression que les épines nasales antérieure et postérieure sont des zones relativement fixes par rapport à la jointure prémaxillopalatine

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Cycles in the chamber homology of GL(3)

Let F be a nonarchimedean local field and let GL(N) = GL(N,F). We prove the existence of parahoric types for GL(N). We construct representative cycles in all the homology classes of the chamber homology of GL(3).Comment: 45 pages. v3: minor correction