30,271 research outputs found
Loop groups and diffeomorphism groups of the circle as colimits
We show that loop groups and the universal cover of
can be expressed as colimits of groups of loops/diffeomorphisms supported in
subintervals of . Analogous results hold for based loop groups and for the
based diffeomorphism group of . These results continue to hold for the
corresponding centrally extended groups.
We use the above results to construct a comparison functor from the
representations of a loop group conformal net to the representations of the
corresponding affine Lie algebra. We also establish an equivalence of
categories between solitonic representations of the loop group conformal net,
and locally normal representations of the based loop group.Comment: updated to published versio
A Periodicity Theorem for the Octahedron Recurrence
We investigate a variant of the octahedron recurrence which lives in a
3-dimensional lattice contained in [0,n] x [0,m] x R. Generalizing results of
David Speyer math.CO/0402452, we give an explicit non-recursive formula for the
values of this recurrence in terms of perfect matchings. We then use it to
prove that the octahedron recurrence is periodic of period n+m. This result is
reminiscent of Fomin and Zelevinsky's theorem about the periodicity of
Y-systems.Comment: 22 pages, (a few pictures added, section 3 has been reorganized
What Chern-Simons theory assigns to a point
In this note, we answer the questions "What does Chern-Simons theory assign
to a point?" and "What kind of mathematical object does Chern-Simons theory
assign to a point?".
Our answer to the first question is representations of the based loop group.
More precisely, we identify a certain class of projective unitary
representations of the based loop group that we locally normal
representations. We define the fusion product of such representations and we
prove that, modulo certain conjectures, the Drinfel'd centre of that
representation category of is equivalent to the category of positive
energy representations of the free loop group . The above mentioned
conjectures are known to hold when the gauge group is abelian or of type .
Our answer to the second question is bicommutant categories. The latter are
higher categorical analogs of von Neumann algebras: they are tensor categories
that are equivalent to their bicommutant inside , the category
of bimodules over a hyperfinite factor. We prove that, modulo
certain conjectures, the category of locally normal representations of the
based loop group is a bicommutant category. The relevant conjectures are known
to hold when the gauge group is abelian or of type .
Our work builds on the formalism of coordinate free conformal nets, developed
jointly with A. Bartels and C. Douglas.Comment: Minor changes. Added a summary diagram at the end. Replaced the
terminology "positive energy representations of the based loop group" by
"locally normal representations of the based loop group
Students' Perceptions of their Rights in Portugal
The present study analyses young Portuguese students’perceptions of their rights at school and at home. The sample consisted
of 294 male and female students, in Year 7 to Year 9, from several regions in the country. The assessment instrument used was
the ‘Children’s Rights Scale’ (Hart, 1993; Hart et al., 1996) and results were related to a number of other questions regarding the
following independent variables: (1) school variables (school year, school achievement, teacher’s support, violence at school); (2) family variables (parental authority, family cohesion, parents’ education);
(3) personal variables (age, gender, professional interests). Significant
relations were found between the students’ perceptions of their rights and these independent variables. In general, Portuguese
students declare that their rights exist and are very important.
Students who have a greater degree of personal limitations, or who live in worse school or family contexts, are the ones who indicate less importance and perceive less existence of rights at school and at
home. The study gives directions to efforts to strengthen projects for the promotion of students’ rights by including training programs for teachers and parents, in a close net connection among school, family
and significant social agents.This study was financed by JNICT/FCT and by the PRAXIS XXI Program for the
period from 1997 to 2002 and developed at the Center for Research in Education
of the Faculty of Sciences of the University of Lisbon (CIEFCUL)R. Ernesto
Vasconcelos, Edif. C1–2º, 1749–016 Lisbon, Portugal
Loop quantum cosmology and the Wheeler-De Witt equation
We present some results concerning the large volume limit of loop quantum
cosmology in the flat homogeneous and isotropic case. We derive the Wheeler-De
Witt equation in this limit. Looking for the action from which this equation
can also be obtained, we then address the problem of the modifications to be
brought to the Friedman's equation of motion and to the equation of motion of
the scalar field, in the classical limit.Comment: 17 pages; 5 figure
- …