43 research outputs found
Fusion Rules and R-Matrices For Representations of at Roots of Unity
We recall the classification of the irreducible representations of ,
and then give fusion rules for these representations. We also consider the
problem of \cR-matrices, intertwiners of the differently ordered tensor
products of these representations, and satisfying altogether Yang--Baxter
equations.Comment: 13 pages. This is a contribution to the Vth Conference on
Mathematical Physics, Edirne, Turkey 15-22 Dec. 199
New fusion rules and \cR-matrices for at roots of unity
We derive fusion rules for the composition of -deformed classical
representations (arising in tensor products of the fundamental representation)
with semi-periodic representations of at roots of unity. We obtain
full reducibility into semi-periodic representations. On the other hand,
heterogeneous \cR-matrices which intertwine tensor products of periodic or
semi-periodic representations with -deformed classical representations are
given. These \cR-matrices satisfy all the possible Yang Baxter equations with
one another and, when they exist, with the \cR-matrices intertwining
homogeneous tensor products of periodic or semi-periodic representations. This
compatibility between these two kinds of representations has never been used in
physical models.Comment: 12 page
Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians
We examine the two parameter deformed superalgebra and use
the results in the construction of quantum chain Hamiltonians. This study is
done both in the framework of the Serre presentation and in the -matrix
scheme of Faddeev, Reshetikhin and Takhtajan (FRT). We show that there exists
an infinite number of Casimir operators, indexed by integers in the
undeformed case and by in the deformed case, which obey quadratic
relations. The construction of the dual superalgebra of functions on
is also given and higher tensor product representations are
discussed. Finally, we construct quantum chain Hamiltonians based on the
Casimir operators. In the deformed case we find two Hamiltonians which describe
deformed models.Comment: 27 pages, LaTeX, one reference moved and one formula adde
Precursors and Laggards: An Analysis of Semantic Temporal Relationships on a Blog Network
We explore the hypothesis that it is possible to obtain information about the
dynamics of a blog network by analysing the temporal relationships between
blogs at a semantic level, and that this type of analysis adds to the knowledge
that can be extracted by studying the network only at the structural level of
URL links. We present an algorithm to automatically detect fine-grained
discussion topics, characterized by n-grams and time intervals. We then propose
a probabilistic model to estimate the temporal relationships that blogs have
with one another. We define the precursor score of blog A in relation to blog B
as the probability that A enters a new topic before B, discounting the effect
created by asymmetric posting rates. Network-level metrics of precursor and
laggard behavior are derived from these dyadic precursor score estimations.
This model is used to analyze a network of French political blogs. The scores
are compared to traditional link degree metrics. We obtain insights into the
dynamics of topic participation on this network, as well as the relationship
between precursor/laggard and linking behaviors. We validate and analyze
results with the help of an expert on the French blogosphere. Finally, we
propose possible applications to the improvement of search engine ranking
algorithms
Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings
We construct two quantum spin chains Hamiltonians with quantum sl(2|1)
invariance. These spin chains define variants of the Hubbard model and describe
electron models with pair hoppings. A cubic algebra that admits the
Birman-Wenzl-Murakami algebra as a quotient allows exact solvability of the
periodic chain. The two Hamiltonians, respectively built using the
distinguished and the fermionic bases of U_q(sl(2|1)) differ only in the
boundary terms. They are actually equivalent, but the equivalence is non local.
Reflection equations are solved to get exact solvability on open chains with
non trivial boundary conditions. Two families of diagonal solutions are found.
The centre and the Scasimirs of the quantum enveloping algebra of sl(2|1)
appear as tools for the construction of exactly solvable Hamiltonians.Comment: 22 pages, LaTeX2e, uses amsfonts; some references added and typos
correcte
On osp(M|2n) integrable open spin chains
We consider open spin chains based on osp(m|2n) Yangians. We solve the
reflection equations for some classes of reflection matrices, including the
diagonal ones. Having then integrable open spin chains, we write the analytical
Bethe Ansatz equations. More details and references can be found in [1,2].Comment: Talk given by DA at ISQG13, Prague, June 2004 ; to appear in Czech.
J. Phy
Triaxial quadrupole deformation dynamics in sd-shell nuclei around 26Mg
Large-amplitude dynamics of axial and triaxial quadrupole deformation in
24,26Mg, 24Ne, and 28Si is investigated on the basis of the quadrupole
collective Hamiltonian constructed with use of the constrained
Hartree-Fock-Bogoliubov plus the local quasiparticle random phase approximation
method. The calculation reproduces well properties of the ground rotational
bands, and beta and gamma vibrations in 24Mg and 28Si. The gamma-softness in
the collective states of 26Mg and 24Ne are discussed. Contributions of the
neutrons and protons to the transition properties are also analyzed in
connection with the large-amplitude quadrupole dynamics.Comment: 16 pages, 18 figures, submitted to Phys. Rev.
Polynomial Relations in the Centre of U_q(sl(N))
When the parameter of deformation q is a m-th root of unity, the centre of
U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new
generators, which are basically the m-th powers of all the Cartan generators of
U_q(sl(N)). All these central elements are however not independent. In this
letter, generalising the well-known case of U_q(sl(2)), we explicitly write
polynomial relations satisfied by the generators of the centre. Application to
the parametrization of irreducible representations and to fusion rules are
sketched.Comment: 8 pages, minor TeXnical revision to allow automatic TeXin