Simplicity of some twin tree automorphism groups with trivial commutation relations

We prove simplicity for incomplete rank 2 Kac-Moody groups over algebraic closures of finite fields with trivial commutation relations between root groups corresponding to prenilpotent pairs. We don't use the (yet unknown) simplicity of the corresponding finitely generated groups (i.e., when the ground field is finite). Nevertheless we use the fact that the latter groups are just infinite (modulo center).Comment: 10 page

Group-theoretic compactification of Bruhat-Tits buildings

Let GF denote the rational points of a semisimple group G over a non-archimedean local field F, with Bruhat-Tits building X. This paper contains five main results. We prove a convergence theorem for sequences of parahoric subgroups of GF in the Chabauty topology, which enables to compactify the vertices of X. We obtain a structure theorem showing that the Bruhat-Tits buildings of the Levi factors all lie in the boundary of the compactification. Then we obtain an identification theorem with the polyhedral compactification (previously defined in analogy with the case of symmetric spaces). We finally prove two parametrization theorems extending the BruhatTits dictionary between maximal compact subgroups and vertices of X: one is about Zariski connected amenable subgroups, and the other is about subgroups with distal adjoint action

Topological simplicity, commensurator super-rigidity and nonlinearities of Kac-Moody groups (appendix by P. Bonvin)

We provide new arguments to see topological Kac-Moody groups as generalized semisimple groups over local fields: they are products of topologically simple groups and their Iwahori subgroups are the normalizers of the pro-p Sylow subgroups. We use a dynamical characterization of parabolic subgroups to prove that some countable Kac-Moody groups with Fuchsian buildings are not linear. We show for this that the linearity of a countable Kac-Moody group implies the existence of a closed embedding of the corresponding topological group in a non-Archimedean simple Lie group, thanks to a commensurator super-rigidity theorem proved in the Appendix by P. Bonvi

Automorphisms of Drinfeld half-spaces over a finite field

We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the sense of Berkovich over the finite field equipped with the trivial valuation. We also take into account extensions of the base field.Comment: 15 page

BRUHAT-TITS THEORY FROM BERKOVICH'S POINT OF VIEW.<br>I - REALIZATIONS AND COMPACTIFICATIONS OF BUILDINGS

We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group G over a suitable non-Archimedean field k we define a map from the Bruhat-Tits building B(G,k) to the Berkovich analytic space Gan asscociated with G. Composing this map with the projection of G^an to its flag varieties, we define a family of compactifications of B(G,k). This generalizes results by Berkovich in the case of split groups. Moreover, we show that the boundary strata of the compactified buildings are precisely the Bruhat-Tits buildings associated with a certain class of parabolics. We also investigate the stabilizers of boundary points and prove a mixed Bruhat decomposition theorem for them

Depletion of SMN by RNA interference in HeLa cells induces defects in Cajal body formation

Neuronal degeneration in spinal muscular atrophy (SMA) is caused by reduced expression of the survival of motor neuron (SMN) protein. The SMN protein is ubiquitously expressed and is present both in the cytoplasm and in the nucleus where it localizes in Cajal bodies. The SMN complex plays an essential role for the biogenesis of spliceosomal U-snRNPs. In this article, we have used an RNA interference approach in order to analyse the effects of SMN depletion on snRNP assembly in HeLa cells. Although snRNP profiles are not perturbed in SMN-depleted cells, we found that SMN depletion gives rise to cytoplasmic accumulation of a GFP-SmB reporter protein. We also demonstrate that the SMN protein depletion induces defects in Cajal body formation with coilin being localized in multiple nuclear foci and in nucleolus instead of canonical Cajal bodies. Interestingly, the coilin containing foci do not contain snRNPs but appear to co-localize with U85 scaRNA. Because Cajal bodies represent the location in which snRNPs undergo 2′-O-methylation and pseudouridylation, our results raise the possibility that SMN depletion might give rise to a defect in the snRNA modification process