Descent of Equivalences and Character Bijections

Categorical equivalences between block algebras of finite groups—such as Morita and derived equivalences—are well known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for attempting to realise known Morita and derived equivalences over non-splitting fields. This article presents various results on the theme of descent to appropriate subfields and subrings. We start with the observation that perfect isometries induced by a virtual Morita equivalence induce isomorphisms of centres in non-split situations and explain connections with Navarro’s generalisation of the Alperin–McKay conjecture. We show that Rouquier’s splendid Rickard complex for blocks with cyclic defect groups descends to the non-split case. We also prove a descent theorem for Morita equivalences with endopermutation source

The geometry of the limit of N=2 minimal models

We consider the limit of two-dimensional N=(2,2) superconformal minimal models when the central charge approaches c=3. Starting from a geometric description as non-linear sigma models, we show that one can obtain two different limit theories. One is the free theory of two bosons and two fermions, the other one is a continuous orbifold thereof. We substantiate this claim by detailed conformal field theory computations.Comment: 35 pages, 3 figures; v2 minor corrections, version to be published in J. Phys.

Selenium Status in Paediatric Patients with Neurodevelopmental Diseases

Neurodevelopmental diseases are often associated with other comorbidities, especially inflammatory processes. The disease may affect the trace element (TE) status, which in turn may affect disease severity and progression. Selenium (Se) is an essential TE required for the biosynthesis of selenoproteins including the transporter selenoprotein P (SELENOP) and extracellular glutathione peroxidase (GPX3). SELENOP deficiency in transgenic mice resulted in a Se status-dependent phenotype characterized by impaired growth and disturbed neuronal development, with epileptic seizures on a Se-deficient diet. Therefore, we hypothesized that Se and SELENOP deficiencies may be prevalent in paediatric patients with a neurodevelopmental disease. In an exploratory cross-sectional study, serum samples from children with neurodevelopmental diseases (n = 147) were analysed for total serum Se, copper (Cu), and zinc (Zn) concentrations as well as for the TE biomarkers SELENOP, ceruloplasmin (CP), and GPX3 activity. Children with epilepsy displayed elevated Cu and Zn concentrations but no dysregulation of serum Se status. Significantly reduced SELENOP concentrations were found in association with intellectual disability (mean +/- SD (standard deviation); 3.9 +/- 0.9 mg/L vs. 4.4 +/- 1.2 mg/L, p = 0.015). A particularly low GPX3 activity (mean +/- SD; 172.4 +/- 36.5 vs. 192.6 +/- 46.8 U/L, p = 0.012) was observed in phacomatoses. Autoantibodies to SELENOP, known to impair Se transport, were not detected in any of the children. In conclusion, there was no general association between Se deficiency and epilepsy in this observational analysis, which does not exclude its relevance to individual cases. Sufficiently high SELENOP concentrations seem to be of relevance to the support of normal mental development. Decreased GPX3 activity in phacomatoses may be relevant to the characteristic skin lesions and merits further analysis. Longitudinal studies are needed to determine whether the observed differences are relevant to disease progression and whether correcting a diagnosed TE deficiency may confer health benefits to affected children

B-type defects in Landau-Ginzburg models

We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W=X^d and W=X^d+Z^2 are analysed in detail, and the results are compared to the CFT treatment of defects in N=2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.Comment: 50 pages, 2 figure