The coisotropic subgroup structure of SL_q(2,R)

We study the coisotropic subgroup structure of standard SL_q(2,R) and the corresponding embeddable quantum homogeneous spaces. While the subgroups S^1 and R_+ survive undeformed in the quantization as coalgebras, we show that R is deformed to a family of quantum coisotropic subgroups whose coalgebra can not be extended to an Hopf algebra. We explicitly describe the quantum homogeneous spaces and their double cosets.Comment: LaTex2e, 10pg, no figure

Quantization of Projective Homogeneous Spaces and Duality Principle

We introduce a general recipe to construct quantum projective homogeneous spaces, with a particular interest for the examples of the quantum Grassmannians and the quantum generalized flag varieties. Using this construction, we extend the quantum duality principle to quantum projective homogeneous spaces.Comment: Final version (after correcting the journal's proofs), to appear in "Journal of Noncommutative Geometry

Quantum planes and quantum cylinders from Poisson homogeneous spaces

Quantum planes and a new quantum cylinder are obtained as quantization of Poisson homogeneous spaces of two different Poisson structures on classical Euclidean group E(2).Comment: 13 pages, plain Tex, no figure

q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation

Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group

After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The canonical action of Eq(2) is used to define a natural q-analog of the free Schro"dinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of two q-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in the qP case, are given in terms of Hahn-Exton functions. Introducing the universal T-matrix for Eq(2) we prove that the Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix elements of T, thus giving the correct extension to quantum groups of well known methods in harmonic analysis.Comment: 19 pages, plain tex, revised version with added materia

Persistent Unresolved Inflammation in the Mecp2-308 Female Mutated Mouse Model of Rett Syndrome

Rett syndrome (RTT) is a rare neurodevelopmental disorder usually caused by mutations in the X-linked gene methyl-CpG-binding protein 2 (MECP2). Several Mecp2 mutant mouse lines have been developed recapitulating part of the clinical features. In particular, Mecp2-308 female heterozygous mice, bearing a truncating mutation, are a validated model of the disease. While recent data suggest a role for inflammation in RTT, little information on the inflammatory status in murine models of the disease is available. Here, we investigated the inflammatory status by proteomic 2-DE/MALDI-ToF/ToF analyses in symptomatic Mecp2-308 female mice. Ten differentially expressed proteins were evidenced in the Mecp2-308 mutated plasma proteome. In particular, 5 positive acute-phase response (APR) proteins increased (i.e., kininogen-1, alpha-fetoprotein, mannose-binding protein C, alpha-1-antitrypsin, and alpha-2-macroglobulin), and 3 negative APR reactants were decreased (i.e., serotransferrin, albumin, and apolipoprotein A1). CD5 antigen-like and vitamin D-binding protein, two proteins strictly related to inflammation, were also changed. These results indicate for the first time a persistent unresolved inflammation of unknown origin in the Mecp2-308 mouse model

Representations of Quantum Bicrossproduct Algebras

We present a method to construct induced representations of quantum algebras having the structure of bicrossproduct. We apply this procedure to some quantum kinematical algebras in (1+1)--dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum kappa Galilei algebra.Comment: LaTeX 2e, 35 page

MtDNA mutagenesis impairs elimination of mitochondria during erythroid maturation leading to enhanced erythrocyte destruction

Haematopoietic progenitor cells show special sensitivity to mitochondrial DNA (mtDNA) mutagenesis, which suggests that increased mtDNA mutagenesis could underlie anemias. Here we show that elevated mtDNA mutagenesis in mice with a proof-reading deficient mtDNA polymerase (PolG) leads to incomplete mitochondrial clearance, with asynchronized iron loading in erythroid precursors, and increased total and free cellular iron content. The resulting Fenton chemistry leads to oxidative damage and premature destruction of erythrocytes by splenic macrophages. Our data indicate that mitochondria actively contribute to their own elimination in reticulocytes and modulate iron loading. Asynchrony of this sequence of events causes severe mitochondrial anaemia by depleting the organism of red blood cells and the bone marrow of iron. Our findings account for the anaemia development in a progeroid mouse model and may have direct relevance to the anemias associated with human mitochondrial disease and ageing.Peer reviewe