Abstract involutions of algebraic groups and of Kac-Moody groups

Based on the second author's thesis in this article we provide a uniform treatment of abstract involutions of algebraic groups and of Kac-Moody groups using twin buildings, RGD systems, and twisted involutions of Coxeter groups. Notably we simultaneously generalize the double coset decompositions established by Springer and by Helminck-Wang for algebraic groups and by Kac-Wang for certain Kac-Moody groups, we analyze the filtration studied by Devillers-Muhlherr in the context of arbitrary involutions, and we answer a structural question on the combinatorics of involutions of twin buildings raised by Bennett-Gramlich-Hoffman-Shpectorov

Regulation of Macrophage Motility by the Water Channel Aquaporin-1: Crucial Role of M0/M2 Phenotype Switch

The water channel aquaporin-1 (AQP1) promotes migration of many cell types. Although AQP1 is expressed in macrophages, its potential role in macrophage motility, particularly in relation with phenotype polarization, remains unknown. We here addressed these issues in peritoneal macrophages isolated from AQP1-deficient mice, either undifferentiated (M0) or stimulated with LPS to orientate towards pro-inflammatory phenotype (classical macrophage activation; M1). In non-stimulated macrophages, ablation of AQP1 (like inhibition by HgCl2) increased by 2-3 fold spontaneous migration in a Src/PI3K/Rac-dependent manner. This correlated with cell elongation and formation of lamellipodia/ruffles, resulting in membrane lipid and F4/80 recruitment to the leading edge. This indicated that AQP1 normally suppresses migration of resting macrophages, as opposed to other cell types. Resting Aqp1-/- macrophages exhibited CD206 redistribution into ruffles and increased arginase activity like IL4/IL13 (alternative macrophage activation; M2), indicating a M0-M2 shift. In contrast, upon M1 orientation by LPS in vitro or peritoneal inflammation in vivo , migration of Aqp1-/- macrophages was reduced. Taken together, these data indicate that AQP1 oppositely regulates macrophage migration, depending on stimulation or not by LPS, and that macrophage phenotypic and migratory changes may be regulated independently of external cues

Iwasawa decompositions of split Kac-Moody groups

We characterize all fields F for which a group with an F-locally split root group datum admits an Iwasawa decomposition. This class of groups in particular includes the split semisimple algebraic groups and the split Kac-Moody groups

Moufang sets of type F-4

We give an explicit description of the Moufang sets of type F-4, i.e. the buildings arising from the simple algebraic groups of absolute type F4 and relative rank one, over an arbitrary field. We use octonion planes and certain polarities to find this description, and we rely on the theory of Albert algebras. We also determine the automorphism groups of the corresponding exceptional unitals, thereby completing the program of J. Tits for these non-abelian Moufang sets. In particular we prove that every automorphism of that unital is induced by a collineation of the ambient projective plane