Fusion Rules and R-Matrices For Representations of SL(2)qSL(2)_q at Roots of Unity

We recall the classification of the irreducible representations of $SL(2)_q$, 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 SL(N)qSL(N)_q at roots of unity

We derive fusion rules for the composition of $q$-deformed classical representations (arising in tensor products of the fundamental representation) with semi-periodic representations of $SL(N)_q$ 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 $q$-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 $U_{qs}(sl(1|2))$ 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 $R$-matrix scheme of Faddeev, Reshetikhin and Takhtajan (FRT). We show that there exists an infinite number of Casimir operators, indexed by integers $p > 1$ in the undeformed case and by $p \in Z$ in the deformed case, which obey quadratic relations. The construction of the dual superalgebra of functions on $SL_{qs}(1|2)$ 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 $t-J$ 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