Plethystic Vertex Operators and Boson-Fermion Correspondences

We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape \pi. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each \pi, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.Comment: 21 pages, LaTeX. Minor typos corrected. Added brief survey of related work and new reference

The Hopf Algebra Structure of the Character Rings of Classical Groups

The character ring \CGL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra \Sym$ of symmetric functions. Here we study the character rings \CO and \CSp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that \CO and \CSp also admit natural Hopf algebra structures that are isomorphic to that of \CGL, and hence to \Sym. The isomorphisms are determined explicitly, along with the specification of standard bases for \CO and \CSp analogous to those used for \Sym. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur-Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the \CGL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras \CO and \CSp are not self-dual. The dual Hopf algebras \CO^* and \CSp^* are identified. Finally, the Hopf algebra of the universal rational character ring \CGLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified.Comment: 38 pages, uses pstricks; new version is a major update, new title, new material on rational character

Predicting the effects of sand erosion on collector surfaces in CSP plants

This paper presents a methodology to predict the optical performance and physical topography of the glass collector surfaces of any given CSP plant in the presence of sand and dust storms, providing that local climate conditions are known and representative sand and dust particles samples are available. Using existing meteorological data for a defined CSP plant in Egypt, plus sand and dust samples from two desert locations in Libya, we describe how to derive air speed, duration, and sand concentrations to use within the Global CSP Laboratory sand erosion simulation rig at Cranfield University. This then allows us to predict the optical performance of parabolic trough collector glass after an extended period by the use of accelerated ageing. However the behavior of particles in sandstorms is complex and has prompted a theoretical analysis of sand particle dynamics which is also described in this paper

Plethystic vertex operators and boson-fermion correspondences

We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopfalgebraic structure of certain symmetric function series and their plethysms

The impact of cafeteria feeding during lactation in the rat on novel object discrimination in the offspring

There is increasing evidence that hyperenergetic diets impact on memory in rodents. However, it is largely unknown how diets, such as a cafeteria diet (CD), that mimic a Western diet act on learning and memory, in particular when fed during early stages of development. Here, we fed lactating dams a cafeteria diet and exposed both male and female offspring to a novel object discrimination (NOD) task, a two-trial test of recognition memory in which rats exposed to two identical objects during a training/familiarisation trial can discriminate a novel from a familiar object during the subsequent choice trial. The choice trial was performed following inter-trial interval (ITI) delays of up to 4 h. Maternal diet did not impact on exploration of the objects by either sex during the familiarisation trial. Control males discriminated the novel from the familiar object indicating intact memory with an ITI of 1h, but not 2 or 4h. CD delayed this natural forgetting in male rats such that discrimination was also evident after a 2h ITI. In contrast, control females exhibited discrimination following both 1 and 2h ITIs, but CD impaired performance. In summary, the present study shows that maternal exposure to CD programmes NOD in the adult. In better performing females dietary programming interferes with NOD whereas NOD was improved in males after lactational CD feeding

The problem of overskilling in Australia and Britain

This paper examines the parallel trends in education and labour market developments in Australia and Britain. It uses unique information in the WERS and HILDA surveys on reported overskilling in the workplace. To a degree, the overskilling information overcomes the problem of unobserved ability differences and focuses on the actual job-employee mismatch more than the conventional overeducation variables can. The paper finds that the prevalence of overskilling decreases with education at least for Australia, but the wage penalty associated with overskilling increases with education. Although the general patterns of overskilling (prevalence and penalties) are fairly similar between Australia and Britain, the problem appears to be greater in Britain