17,134 research outputs found

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

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    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

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    Let \H_n be the Iwahori-Hecke algebra of the symmetric group SnS_n, and let Z(\H_n) denote its centre. Let B=b1,b2,...,btB={b_1,b_2,...,b_t} be a basis for Z(\H_n) over R=Z[q,q1]R=\Z[q,q^{-1}]. Then BB is called \emph{multiplicative} if, for every ii and jj, there exists kk such that bibj=bkb_ib_j= b_k. In this article we prove that there are no multiplicative bases for Z(ZSn)Z(\Z S_n) and Z(\H_n) when n3n\ge 3. In addition, we prove that there exist exactly two multiplicative bases for Z(ZS2)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

    Life in the eucharistic community : an empirical study in psychological type theory and biblical hermeneutics reading John 6:5–15

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    This study employs psychological type theory to analyse the ways in which a group of 13 newly ordained Anglican priests (in priest’s orders for 3 or 4 months) reflected on the Eucharistic imagery of the Johannine feeding narrative. In the first exercise, the priests worked in two groups distinguished according to their perceiving preference (7 sensing types and 6 intuitive types). In the second exercise, the priests worked in three groups distinguished according to their judging preferences (4 thinking types, 4 feeling types, and 5 feeling types). The data supported the significance of psychological type in shaping the hermeneutical process (the theory underpinning the SIFT method of biblical hermeneutics and liturgical preaching). Sensing types grappled with the plethora of detail within the text. Intuitive types looked for the bigger picture and identified major themes. Thinking types looked for and organised the major issues raised by the passage. Feeling types focused on the human and relational implications of the narrative

    Exploring the limits of multiplexed photon-pair sources for the preparation of pure single-photon states

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    Current sources of heralded single photons based on nonlinear optics operate in a probabilistic manner. In order to build quantum-enhanced devices based around the use of single photons, compact, turn-key and deterministic sources are required. A possible solution is to multiplex a number of sources to increase the single-photon generation probability and in so doing reducing the waiting time to deliver large numbers of photons simultaneously, from independent sources. Previously it has been shown that, in the ideal case, 17 multiplexed sources allow deterministic generation of heralded single photons [Christ and Silberhorn, Phys. Rev. A 85, 023829 (2012)]. Here we extend this analysis to include undesirable effects of detector inefficiency and photon loss on a number of multiplexed sources using a variety of different detectors for heralding. We compare these systems for fixed signal-to-noise ratio to allow a direct comparison of performance for real- world heralded single photon sources.Comment: 10 pages, 7 figures. Equation 18 changed to include power of a half in the binomial facto

    Temporal Loop Multiplexing: A resource efficient scheme for multiplexed photon-pair sources

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    Single photons are a vital resource for photonic quantum information processing. However, even state-of-the-art single photon sources based on photon-pair generation and heralding detection have only a low probability of delivering a single photon when one is requested. We analyse a scheme that uses a switched fibre delay loop to increase the delivery probability per time bin of single photons from heralded sources. We show that, for realistic experimental parameters, combining the output of up to 15 pulses can yield a performance improvement of a factor of 10. We consider the future performance of this scheme with likely component improvements.Comment: 5 pages, 4 figure

    An anatomy of change : profiling cohort difference in beliefs and attitudes among Anglicans in England

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    Conservatism in theological belief, moral values and attitude toward ecclesiastical practices was measured in a sample of 5967 ordained and lay Anglicans in the Church of England. Average scores were compared between those who classed themselves as Anglo-catholic, broad church or evangelical, and by six different age cohorts. Overall, most measures of conservatism showed decline among more recent cohorts, but there were marked differences between traditions. Younger evangelicals showed little or no decline in theological or moral conservatism, and, in the case of Bible beliefs, were more conservative than their older counterparts. In ecclesiastical variables, however, Anglo-catholics were often more conservative and younger evangelicals showed less conservatism than other traditions or older evangelicals. The findings suggest that the divide between traditions is increasing among younger generations mainly because those in Anglo-catholic and broad-church traditions are becoming more liberal on theological or moral matters, whereas evangelicals are maintaining traditional conservative views of theology and morality but becoming less traditional in matters ecclesiastical