46 research outputs found
On representation theory of quantum groups at roots of unity
Irreducible representations of quantum groups (in Woronowicz'
approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of
being an~odd root of unity. Here we find the~irreducible representations
for all roots of unity (also of an~even degree), as well as describe
"the~diagonal part" of tensor product of any two irreducible representations.
An~example of not completely reducible representation is given. Non--existence
of Haar functional is proved. The~corresponding representations of universal
enveloping algebras of Jimbo and Lusztig are provided. We also recall the~case
of general~. Our computations are done in explicit way.Comment: 31 pages, Section 2.7 added and other minor change
Fusion Rules of the Lowest Weight Representations of osp_q(1|2) at Roots of Unity: Polynomial Realization and Degeneration at Roots of Unity
The degeneracy of the lowest weight representations of the quantum
superalgebra and their tensor products at exceptional values of
%when deformation parameter takes exceptional values is studied. The main
features of the structures of the finite dimensional lowest weight
representations and their fusion rules are illustrated using realization of
group generators as finite-difference operators acting in the space of the
polynomials. The complete fusion rules for the decompositions of the tensor
products at roots of unity are presented. The appearance of indecomposable
representations in the fusions is described using Clebsh-Gordan coefficients
derived for general values of and at roots of unity.Comment: 28 pages, 3 figures; completed (section 5, section 6); version
published in JP
Duality for Exotic Bialgebras
In the classification of Hietarinta, three triangular
-matrices lead, via the FRT formalism, to matrix bialgebras which are not
deformations of the trivial one. In this paper, we find the bialgebras which
are in duality with these three exotic matrix bialgebras. We note that the
duality of FRT is not sufficient for the construction of the bialgebras
in duality. We find also the quantum planes corresponding to these bialgebras
both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq
Lectin-Dependent Enhancement of Ebola Virus Infection via Soluble and Transmembrane C-type Lectin Receptors
Mannose-binding lectin (MBL) is a key soluble effector of the innate immune system that recognizes pathogen-specific surface glycans. Surprisingly, low-producing MBL genetic variants that may predispose children and immunocompromised individuals to infectious diseases are more common than would be expected in human populations. Since certain immune defense molecules, such as immunoglobulins, can be exploited by invasive pathogens, we hypothesized that MBL might also enhance infections in some circumstances. Consequently, the low and intermediate MBL levels commonly found in human populations might be the result of balancing selection. Using model infection systems with pseudotyped and authentic glycosylated viruses, we demonstrated that MBL indeed enhances infection of Ebola, Hendra, Nipah and West Nile viruses in low complement conditions. Mechanistic studies with Ebola virus (EBOV) glycoprotein pseudotyped lentiviruses confirmed that MBL binds to N-linked glycan epitopes on viral surfaces in a specific manner via the MBL carbohydrate recognition domain, which is necessary for enhanced infection. MBL mediates lipid-raft-dependent macropinocytosis of EBOV via a pathway that appears to require less actin or early endosomal processing compared with the filovirus canonical endocytic pathway. Using a validated RNA interference screen, we identified C1QBP (gC1qR) as a candidate surface receptor that mediates MBL-dependent enhancement of EBOV infection. We also identified dectin-2 (CLEC6A) as a potentially novel candidate attachment factor for EBOV. Our findings support the concept of an innate immune haplotype that represents critical interactions between MBL and complement component C4 genes and that may modify susceptibility or resistance to certain glycosylated pathogens. Therefore, higher levels of native or exogenous MBL could be deleterious in the setting of relative hypocomplementemia which can occur genetically or because of immunodepletion during active infections. Our findings confirm our hypothesis that the pressure of infectious diseases may have contributed in part to evolutionary selection of MBL mutant haplotypes