Irreducible representations of the quantum analogue of SU(2) (2007)
We give the complete set of irreducible representations of U(SU(2))_q when q is a m-th root of unity. In particular we show that their dimensions are less or equal to m. Some of them are not highest...
Quantum Dynamical coBoundary Equation for finite dimensional simple Lie algebras (2005)
Buffenoir, E., Roche, Ph., Terras, V.
For a finite dimensional simple Lie algebra g, the standard universal solution R(x) in $U_q(g)^{\otimes 2}$ of the Quantum Dynamical Yang--Baxter Equation can be built from the standard R--matrix and...
We study the quantization of Chern-Simons theory with group $G$ coupled to dynamical sources. We first study the dynamics of Chern-Simons sources in the Hamiltonian framework. The gauge group of this...
Hamiltonian Analysis of Plebanski Theory (2004)
Buffenoir, E., Henneaux, M., Noui, K., Roche, Ph.
We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non regular, i.e. the rank of the...
An infinite product formula for $U_q(sl(2))$ dynamical coboundary element (2003)
We give a short summary of results and conjectures in the theory of dynamical quantum group related to the dynamical coboundary equation also known as IRF-Vertex transform. O.Babelon has shown that...
Irreducible representations of the quantum analogue of SU(2) (2003)
We give the complete set of irreducible representations of U(SU(2))_q when q is a m-th root of unity. In particular we show that their dimensions are less or equal to m. Some of them are not highest...
We study the tensor product of principal unitary representations of the quantum Lorentz group, prove a decomposition theorem and compute the associated intertwiners. We show that these intertwiners...
Universal Solutions of Quantum Dynamical Yang--Baxter Equations (1997)
D. Arnaudon, E. Buffenoir, E. Ragoucy, Ph. Roche
We construct a universal trigonometric solution of the Gervais--Neveu--Felder equation in the case of finite dimensional simple Lie algebras and finite dimensional contragredient simple Lie...
Universal Solutions of Quantum Dynamical Yang-Baxter Equations (1997)
Arnaudon, D., Buffenoir, E., Ragoucy, E., Roche, Ph.
We construct a universal trigonometric solution of the Gervais-Neveu-Felder equation in the case of finite dimensional simple Lie algebras and finite dimensional contragredient simple Lie...
Harmonic Analysis on the quantum Lorentz group (1997)
This work begins with a review of complexification and realification of Hopf algebras. We emphasize the notion of multiplier Hopf algebras for the description of different classes of functions...
Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory (1995)
We define and study the properties of observables associated to any link in $\Sigma\times {\bf R}$ (where $\Sigma$ is a compact surface) using the combinatorial quantization of hamiltonian...