On bases of centres of Iwahori-Hecke algebras of the symmetric group

Using norms, the second author constructed a basis for the centre of the Hecke algebra of the symmetric group over \Q[\xi] in 1990. An integral "minimal" basis was later given by the first author in 1999, following work of Geck and Rouquier. In principle one can then write elements of the norm basis as integral linear combinations of minimal basis elements. In this paper we find an explicit non-recursive expression for the coefficients appearing in these linear combinations. These coefficients are expressed in terms of readily computable numbers involving orders of symmetric groups and conjugacy classes. In the process of establishing this main theorem, we prove the following items of independent interest: a result on the projection of the norms onto parabolic subalgebras, the existence of an inner product on the Hecke algebra with some interesting properties, and the existence of a partial ordering on the norms.Comment: 29 pages. To appear J. Algebra. Original version January 200

Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group

Let \H_n be the Iwahori-Hecke algebra of the symmetric group $S_n$, and let Z(\H_n) denote its centre. Let $B={b_1,b_2,...,b_t}$ be a basis for Z(\H_n) over $R=\Z[q,q^{-1}]$. Then $B$ is called \emph{multiplicative} if, for every $i$ and $j$, there exists $k$ such that $b_ib_j= b_k$. In this article we prove that there are no multiplicative bases for $Z(\Z S_n)$ and Z(\H_n) when $n\ge 3$. In addition, we prove that there exist exactly two multiplicative bases for $Z(\Z S_2)$ and none for Z(\H_2).Comment: 6 pages. To appear in Proceedings of the Southeastern Lie Theory Workshop Series, Proceedings of Symposia in Pure Mathematic

The visibility of mission agencies in general and USPG in particular among recently ordained Anglican clergy : an empirical enquiry

Attitudes toward mission agencies in general, and toward the United Society for the Propagation of the Gospel (USPG) in particular, were assessed using two 10-item scales completed by 833 recently ordained Anglican clergy from the UK. Clergy were generally positive toward mission agencies and willing for their churches to engage with them, but more reluctant to form personal links. Most clergy felt agencies should give priority to the relief of poverty and to development needs, rather than to spreading specifically Christian beliefs. Results for the USPG indicated more uncertain responses than for mission agencies generally, which probably indicated a lower visibility for this agency among some clergy, especially evangelicals

Attitude toward homosexuality among Anglicans in England: the effects of theological orientation and personality

Disapproval of homosexuality (homonegativity) was assessed using a four-item summated scale in a sample of 7,295 readers of the Church Times who were regular worshippers at Anglican churches in England. The theological orientation of respondents was assessed on three scales measuring preference for liberal or conservative, catholic or evangelical, and charismatic or non-charismatic expressions of faith. Individual differences in personality were assessed using the abbreviated form of the Eysenck Personality Questionnaire Revised (EPQR-A). Scores on the homonegativity scale were generally high, indicating disapproval of same-sex intercourse, same-sex marriage and the ordination or consecration of practising homosexuals. After allowing for sex and age, the main predictors of homonegativity were the three measures of individual theological orientation, each having an independent and additive effect. All four scales of the EPQR-A predicted homonegativity to some extent, but the most important relationships were a negative correlation with the psychoticism scale and a positive correlation with the lie scale. In liberal catholic and broad churches, it appeared that those who were psychologically most susceptible to social conditioning were most likely to be homonegative, but this was not the case in conservative evangelical churches

Which phylogenetic networks are merely trees with additional arcs?

A binary phylogenetic network may or may not be obtainable from a tree by the addition of directed edges (arcs) between tree arcs. Here, we establish a precise and easily tested criterion (based on `2-SAT') that efficiently determines whether or not any given network can be realized in this way. Moreover, the proof provides a polynomial-time algorithm for finding one or more trees (when they exist) on which the network can be based. A number of interesting consequences are presented as corollaries; these lead to some further relevant questions and observations, which we outline in the conclusion.Comment: The final version of this article will appear in Systematic Biology. 20 pages, 7 figure

The psychological temperament of Anglican clergy in ordained local ministry (OLM) : the conserving, serving pastor?

This study draws on psychological type theory as originally proposed by Jung (1971) and psychological temperament theory as proposed by Keirsey and Bates (1978) to explore the hypothesis that ordained local ministers (OLMs) within the Church of England reflect a psychological profile more in keeping with the profile of Church of England congregations than with the profile of established professional mobile clergy serving in the Church of England. Data provided by 135 individuals recently ordained as OLMs (79 women and 56 men) supported the hypothesis. Compared with established professional mobile clergy there is a higher proportion of the Epimethean Temperament (SJ) among OLMs. Oswald and Kroeger (1988) characterise SJ religious leaders as ‘the conserving, serving pastor’. The implications of these findings are discussed for the evolving ministry of the Church of England

All in the mind? : psychological, social and religious predictors of civic volunteerism among churchgoers in England

A number of studies have shown links between volunteerism and a range of sociological and religious variables, mostly based on work from the USA. This study of volunteering among 5220 lay Anglicans in England tested the idea that individual differences in personality could predict civic participation even after allowing for the effects of socio-demographic and religious variables on civic participation. Extraversion significantly increased the probability of civic participation, and the number of different areas of activity among those who did participate. Emotional stability (Neuroticism scale) also significantly increased the chances of volunteering, but not the number of areas of activity among participants. Tender- versus tough-mindedness (Psychoticism scale) had no influence on civic participation in what was a generally tender-minded sample. The results suggest that while socio-demographic factors may affect the opportunities for civic participation, personality and theological orientation may affect the propensity of individuals to participate