On representations of super coalgebras

The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear supergroups serve as an explicit illustration and the simplest example is carried out in detail.Comment: 18 pages, LaTeX, KCL-TH-94-

Massless particles on supergroups and AdS3 x S3 supergravity

Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the quadratic Casimir Hamiltonian becomes diagonalizable in cohomology. We illustrate the general mechanism in detail in the example of a supergroup target GL(1|1). The space of physical states remains an indecomposable infinite dimensional representation of the space-time supersymmetry algebra. Secondly, we show how the full string BRST cohomology in the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir diagonalizable, and reduces the Hilbert space to finite dimensional representations of the space-time supersymmetry algebra (after analytic continuation). Our analysis provides an efficient way to calculate the Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step towards the identification of an interesting and simpler subsector of logarithmic supergroup conformal field theories, relevant to string theory.Comment: 16 pages, 10 figure

Low-frequency variation in TP53 has large effects on head circumference and intracranial volume.

Cranial growth and development is a complex process which affects the closely related traits of head circumference (HC) and intracranial volume (ICV). The underlying genetic influences shaping these traits during the transition from childhood to adulthood are little understood, but might include both age-specific genetic factors and low-frequency genetic variation. Here, we model the developmental genetic architecture of HC, showing this is genetically stable and correlated with genetic determinants of ICV. Investigating up to 46,000 children and adults of European descent, we identify association with final HC and/or final ICV + HC at 9 novel common and low-frequency loci, illustrating that genetic variation from a wide allele frequency spectrum contributes to cranial growth. The largest effects are reported for low-frequency variants within TP53, with 0.5 cm wider heads in increaser-allele carriers versus non-carriers during mid-childhood, suggesting a previously unrecognized role of TP53 transcripts in human cranial development