q-Deformed Supersymmetry and Dynamic Magnon Representations

It was recently noted that the dispersion relation for the magnons of planar N=4 SYM can be identified with the Casimir of a certain deformation of the Poincare algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J and su(2|2) x R^2, we derive a q-deformed super-Poincare symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed rest-frame representation. We comment on aspects of the coalgebra structure and some implications for the question of boost-covariance of the S-matrix.Comment: 15 pages, LaTeX; (v2) references adde

Affinization of category O for quantum groups

Let g be a simple Lie algebra. We consider the category ˆO of those modules over the affine quantum group Uq(bg) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category ˆO . In particular, we develop the theory of q-characters and define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.Peer reviewedFinal Accepted Versio

Automotive automation: Investigating the impact on drivers' mental workload

Recent advances in technology have meant that an increasing number of vehicle driving tasks are becoming automated. Such automation poses new problems for the ergonomist. Of particular concern in this paper are the twofold effects of automation on mental workload - novel technologies could increase attentional demand and workload, alternatively one could argue that fewer driving tasks will lead to the problem of reduced attentional demand and driver underload. A brief review of previous research is presented, followed by an overview of current research taking place in the Southampton Driving Simulator. Early results suggest that automation does reduce workload, and that underload is indeed a problem, with a significant proportion of drivers unable to effectively reclaim control of the vehicle in an automation failure scenario. Ultimately, this research and a subsequent program of studies will be interpreted within the framework of a recently proposed theory of action, with a view to maximizing both theoretical and applied benefits of this domain

Elliptical Tempered Stable Distribution and Fractional Calculus

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, with fractional calculus. Finally, some analytical approximations for the probability density function of tempered infinite divisible distribution, which elliptical tempered stable distributions are a subclass of them, are considered.Comment: 16 pages, working pape