17,134 research outputs found

### 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

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

This study employs psychological type theory to analyse the ways in which a group of 13 newly ordained Anglican priests (in priestâ€™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

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

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

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

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