Irreducible Highest Weight Representations Of The Simple n-Lie Algebra

A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra.Comment: 24 pages, 24 figures, mistake in proposition 2.1 correcte

Comparative evaluation of gene delivery devices in primary cultures of rat hepatic stellate cells and rat myofibroblasts

BACKGROUND: The hepatic stellate cell is the primary cell type responsible for the excessive formation and deposition of connective tissue elements during the development of hepatic fibrosis in chronically injured liver. Culturing quiescent hepatic stellate cells on plastic causes spontaneous activation leading to a myofibroblastic phenotype similar to that seen in vivo. This provides a simple model system for studying activation and transdifferentiation of these cells. The introduction of exogenous DNA into these cells is discussed controversially mainly due to the lack of systematic analysis. Therefore, we examined comparatively five nonviral, lipid-mediated gene transfer methods and adenoviral based infection, as potential tools for efficient delivery of DNA to rat hepatic stellate cells and their transdifferentiated counterpart, i.e. myofibroblasts. Transfection conditions were determined using enhanced green fluorescent protein as a reporter expressed under the transcriptional control of the human cytomegalovirus immediate early gene 1 promoter/enhancer. RESULTS: With the use of chemically enhanced transfection methods, the highest relative efficiency was obtained with FuGENE™6 gene mediated DNA transfer. Quantitative evaluation of representative transfection experiments by flow cytometry revealed that approximately 6% of the rat hepatic stellate cells were transfected. None of the transfection methods tested was able to mediate gene delivery to rat myofibroblasts. To analyze if rat hepatic stellate cells and myofibroblasts are susceptible to adenoviral infection, we have inserted the transgenic expression cassette into a recombinant adenoviral type 5 genome as replacement for the E1 region. Viral particles of this replication-deficient Ad5-based reporter are able to infect 100% of rat hepatic stellate cells and myofibroblasts, respectively. CONCLUSIONS: Our results indicate that FuGENE™6-based methods may be optimized sufficiently to offer a feasible approach for gene transfer into rat hepatic stellate cells. The data further demonstrate that adenoviral mediated transfer is a promising approach for gene delivery to these hepatic cells

Nonlinear PDEs for gap probabilities in random matrices and KP theory

Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are intimately related to wave functions for polynomial (Gel'fand-Dickey reductions) or rational reductions of the KP-hierarchy; their Fredholm determinant also satisfies linear PDEs (Virasoro constraints), yielding, in a systematic way, non-linear PDEs for the Fredholm determinant of such kernels. Examples include Fredholm determinants giving the gap probability of some infinite-dimensional diffusions, like the Airy process, with or without outliers, and the Pearcey process, with or without inliers.Comment: Minor revision: accepted for publication on Physica

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.Comment: Latex, 75 pages. Minor corrections. Final version, to appear in the Japanese Journal of Mathematic

Multiple sums and integrals as neutral BKP tau functions

We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are over projective Schur functions $Q_\alpha$ for strict partitions $\alpha$. We consider two types of such sums: weighted sums of $Q_\alpha$ over strict partitions $\alpha$ and sums over products $Q_\alpha Q_\gamma$. In this way we obtain discrete analogues of the beta-ensembles ($\beta=1,2,4$). Continuous versions are represented as multiple integrals. Such sums and integrals are of interest in a number of problems in mathematics and physics.Comment: 16 page

IL-21 receptor antagonist inhibits differentiation of B cells toward plasmablasts upon alloantigen stimulation

Interaction between T follicular helper (Tfh) cells and B cells is complex and involves various pathways, including the production of IL-21 by the Tfh cells. Secretion of IL-21 results in B cell differentiation toward immunoglobulin-producing plasmablasts. In patients after kidney transplantation, the formation of alloantibodies produced by donor antigen-activated B cells are a major cause of organ failure. In this allogeneic response, the role of IL-21-producing Tfh cells that regulate B cell differentiation is unknown. Here, we tested, in an alloantigen-driven setting, whether Tfh cell help signals control B cell differentiation with its dependency on IL-21. Pre-transplantation patient PBMCs were sorted into pure CD4posCXCR5pos Tfh cells and CD19posCD27pos memory B cells and stimulated with donor antigen in the presence or absence of an IL-21 receptor (IL-21R) antagonist (αIL-21R). Donor antigen stimulation initiated expression of the activation markers inducible co-stimulator (ICOS) and programmed death 1 (PD-1) on Tfh cells and a shift toward a mixed Tfh2 and Tfh17 phenotype. The memory B cells underwent class switch recombination and differentiated toward IgM- and IgG-producing plasmablasts. In the presence of αIL-21R, a dose-dependent inhibition of STAT3 phosphorylation was measured in both T and B cells. Blockade of the IL-21R did not have an effect on PD-1 and ICOS expression on Tfh cells but significantly inhibited B cell differentiation. The proportion of plasmablasts decreased by 78% in the presence of αIL-21R. Moreover, s

Viral subversion of selective autophagy is critical for biogenesis of virus replication organelles

Infection by many (+)RNA viruses is accompanied by ER-expansion and membrane remodelling to form viral replication organelles, followed by assembly and secretion of viral progenies. We previously identified that virus-triggered lipophagy was critical for flaviviral assembly, and is driven by the lipid droplet associated protein Ancient ubiquitin protein 1 (Aup1). A ubiquitin conjugating protein Ube2g2 that functions as a co-factor for Aup1 was identified as a host dependency factor in our study. Here we characterized its function: Ube2g2-deficient cells displayed a dramatic reduction in virus production, which could be rescued by reconstituting the wild-type but not the catalytically deficient (C89K) mutant of Ube2g2, suggesting that its enzymatic activity is necessary. Ube2g2 deficiency did not affect entry of virus particles but resulted in a profound loss in formation of replication organelles, and production of infectious progenies. This phenomenon resulted from its dual activity in (i) triggering lipophagy in conjunction with Aup1, and (ii) degradation of ER chaperones such as Herpud1, SEL1L, Hrd1, along with Sec62 to restrict ER-phagy upon Xbp1-IRE1 triggered ER expansion. Our results therefore underscore an exquisite fine-tuning of selective autophagy by flaviviruses that drive host membrane reorganization during infection to enable biogenesis of viral replication organelles