Quiver Varieties, Category O for Rational Cherednik Algebras, and Hecke Algebras

We relate the representations of the rational Cherednik algebras associated with the complex reflection group µℓ ≀ Sn to sheaves on Nakajima quiver varieties associated with extended Dynkin graphs via a Z-algebra construction. This is done so that as the parameters defining the Cherednik algebra vary, the stability conditions defining the quiver variety change. This construction motivates us to use the geometry of the quiver varieties to interpret the ordering function (the c-function) used to define a highest weight structure on category O of the Cherednik algebra. This interpretation provides a natural partial ordering on O which we expect will respect the highest weight structure. This partial ordering has appeared in a conjecture of Yvonne on the composition factors in O and so our results provide a small step towards a geometric picture for that. We also interpret geometrically another ordering function (the a-function) used in the study of Hecke algebras. (The connection between Cherednik algebras and Hecke algebras is provided by the KZ-functor.) This is related to a conjecture of Bonnafé and Geck on equivalence classes of weight functions for Hecke algebras with unequal parameters since the classes should (and do for type B) correspond to the G.I.T. chambers defining the quiver varieties. As a result anything that can be defined via the quiver varieties

Worldsheet Instantons and the amplitude for string pair production in an external field as a WKB exact functional integral

We revisit the problem of charged string pair creation in a constant external electric field. The string states are massive and creation of pairs from the vacuum is a tunnelling process, analogous to the Schwinger process where charged particle-anti-particle pairs are created by an electric field. We find the instantons in the worldsheet sigma model which are responsible for the tunnelling events. We evaluate the sigma model partition function in the multi-instanton sector in the WKB approximation which keeps the classical action and integrates the quadratic fluctuations about the solution. We find that the summation of the result over all multi-instanton sectors reproduces the known amplitude. This suggests that corrections to the WKB limit must cancel. To show that they indeed cancel, we identify a fermionic symmetry of the sigma model which occurs in the instanton sectors and which is associated with collective coordinates. We demonstrate that the action is symmetric and that the interaction action is an exact form. These conditions are sufficient for localization of the worldsheet functional integral onto its WKB limit.Comment: 40 pages; Expanded discussion section, added reference

Diversifying academic and professional identities in higher education: some management challenges

This paper draws on an international study of the management challenges arising from diversifying academic and professional identities in higher education. These challenges include, for instance, the introduction of practice-based disciplines with different traditions such as health and social care, the changing aspirations and expectations of younger generations of staff, a diffusion of management responsibilities and structures, and imperatives for a more holistic approach to the "employment package", including new forms of recognition and reward. It is suggested that while academic and professional identities have become increasingly dynamic and multi-faceted, change is occurring at different rates in different contexts. A model is offered, therefore, that relates approaches to "people management" to different organisational environments, against the general background of increasing resource constraint arising from the global economic downturn

RHIC: From dreams to beams in two decades

This talk traces the history of RHIC over the last two decades, reviewing the scientific motivations underlying its design, and the challenges and opportunities the machine presents.Comment: To be published in Proceedings of Quark Matter '01. 10 pages, 1 figur

Validation of the HEN model for organic laying hens and assessment of nutrition in organic poultry (CTE0202)

Introduction Regulation EC1804/1999 sets out the minimum standards for organic livestock production and UK organic poultry producers have to adhere to for organic poultry. There are several aspects of Regulation EC1804/1999 which are technically and practicably challenging with regards to organic poultry production and most of these relate to feeding organic poultry. The greatest problems relate to the need to feed mainly organic ingredients, there is a future requirement to feed 100% organic ingredients, and the banning of synthetic amino acids in feeds for organic poultry. The issues raised by the introduction of Regulation EC1804/1999 are: 1) how do we match the supply of energy and nutrients to the bird’s needs for health, welfare and performance in a UK organic poultry production system? 2) Do we fully understand the bird’s amino acid needs for metabolic processes and can we meet them when feeding 80% or more organic ingredients? 3) Do UK-grown organic ingredients have lower crude protein and amino acid contents than their non-organic counterparts? If so, this will exacerbate any difficulties in amino acid supply to the birds. 4) What are the implications of Regulation EC1804/1999 in terms of ingredient supply for organic poultry production? These issues were addressed in this project. Firstly by measuring on-farm the hen’s feed metabolisable energy intake responses to temperature in outdoor production systems and examining whether a model (the ADAS HEN model) of inputs (feed metabolisable energy, protein and amino acids) and outputs (egg numbers and weight) could be validated for use in organic egg production systems. If so, this would provide a user-friendly approach for practical decision making at farm level. Secondly, by examining the published literature on recommended nutrient requirements for non-organic poultry and assessing the applicability of the findings to organic poultry. Thirdly, by sampling organically grown crops (wheat, peas and beans) and determining their contents of crude protein and amino acids. Fourthly, by estimating the size of the UK organic poultry flocks and their requirements for organic ingredients. Objectives 1. To validate the HEN model for organic egg production so that the feed energy value relative to protein content may be better matched with feed intake, and energy and nutrient requirements in differing outdoor temperatures. 2. To scope the technical issues relating to the nutrition of organic pullets, laying hens, table birds and breeder flocks. 3. To review the essential amino acid requirements for maintenance, growth, immune system development, behaviour, laying performance, sexual maturity and the risk of prolapse and interpret the relevance of published conventional data to organic poultry production. 4. To examine whether or not there are differences in the contents of crude protein content, lysine, methionine and threonine of organic and non-organic wheat, peas and beans (by analysis). 5. To examine the implications of changes in Regulation EC1804/1999 and Standards (e.g. organic pullet rearing and organic breeder flocks) on the volumes of organic feed ingredients needed for sustained UK organic poultry production (chickens) based on the current sector size. Implication of findings and future work 1. There is an inability to optimise the dietary ratio of metabolisable energy to protein for hens in outdoor production systems, as the hen’s feed metabolisable energy intake responses to low fluctuating outdoor temperatures have not been defined. The implications of this are tempered with respect to organic egg production as the priority when formulating diets is to meet, as far as possible with the limited range of ingredients available, the organic hen’s methionine and lysine requirements, which in practice is resulting in too much crude protein being fed. 2. Feeding excess crude protein will increase the rate of nitrogen excretion from organic poultry, and there will be an increased risk of nitrogen pollution to the air and water environments. 3. Without additional organic methionine-rich protein sources, methionine deficiencies will become more pronounced and more widespread in organic poultry production as the level of permitted non-organic proteinaceous ingredients in the diet fall. This will impact on bird health and welfare. 4. The possibility of lower methionine contents in organically produced wheat, peas and beans will exacerbate problems of methionine supply. 5. There is an urgent need to identify novel sources of organic methionine-rich protein for feeding organic poultry. This is being addressed in Defra-funded project OF0357 ‘Organic egg production – A desk study on sustainable and innovative methods for meeting the hen’s protein requirements’. The project addressed Defra’s policy of supporting the sustainable development of organic poultry production in the UK. The project has provided both Defra and the industry with information about the key scientific and technical problems, and some possible solutions to these problems. Where there are gaps in knowledge it has highlighted future research needs. The move to 100% organic provenance for organic poultry feeds is an important issue for UK consumers