Positive Energy Representations of the Loop Groups of Non Simply Connected Lie Groups

We classify and construct all irreducible positive energy representations of the loop group of a compact, connected and simple Lie group and show that they admit an intertwining action of Diff(S^{1}).Comment: Available from Springer Verlag at http://link.springer.de

Flat Connections and Quantum Groups

We review the Kohno-Drinfeld theorem as well as a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection D on the Cartan subalgebra of a complex, semi-simple Lie algebra g with poles on the root hyperplanes and values in any g-module V. We sketch our proof of this conjecture when g=sl(n) and when g is arbitrary and V is a vector, spin or adjoint representation. We also establish a precise link between the connection D and Cherednik's generalisation of the KZ connection to finite reflection groups.Comment: 20 pages. To appear in the Proceedings of the 2000 Twente Conference on Lie Groups, in a special issue of Acta Applicandae Mathematica

Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra

Let g be a symmetrisable Kac-Moody algebra and V an integrable g-module in category O. We show that the monodromy of the (normally ordered) rational Casimir connection on V can be made equivariant with respect to the Weyl group W of g, and therefore defines an action of the braid group B_W of W on V. We then prove that this action is uniquely equivalent to the quantum Weyl group action of B_W on a quantum deformation of V, that is an integrable, category O-module V_h over the quantum group U_h(g) such that V_h/hV_h is isomorphic to V. This extends a result of the second author which is valid for g semisimple.Comment: One reference added. 48 page

Development of binder system for manufacturing metallic and ceramic parts by Powder Injection Molding technology

The technology is used by manufacturing companies of metallic and ceramic parts. The PIM companies have an important problem: they have to use a patented feedstock. This fact causes an increasing of the cost of final product. Moreover sometimes is difficult to obtain parts from several materials because only exists few commercial feedstocks. We offer some innovative aspects, the possibility of development of feedstocks from different ceramic and metallic powders and different morphologic and surface characteristics

Quasi-Coxeter categories and a relative Etingof-Kazhdan quantization functor

Let g be a symmetrizable Kac-Moody algebra and U_h(g) its quantized enveloping algebra. The quantum Weyl group operators of U_h(g) and the universal R-matrices of its Levi subalgebras endow U_h(g) with a natural quasi-Coxeter quasitriangular quasibialgebra structure which underlies the action of the braid group of g and Artin's braid groups on the tensor product of integrable, category O modules. We show that this structure can be transferred to the universal enveloping algebra Ug[[h]]. The proof relies on a modification of the Etingof-Kazhdan quantization functor, and yields an isomorphism between (appropriate completions of) U_h(g) and Ug[[h]] preserving a given chain of Levi subalgebras. We carry it out in the more general context of chains of Manin triples, and obtain in particular a relative version of the Etingof-Kazhdan functor with input a split pair of Lie bialgebras. Along the way, we develop the notion of quasi-Coxeter categories, which are to generalized braid groups what braided tensor categories are to Artin's braid groups. This leads to their succint description as a 2-functor from a 2-category whose morphisms are De Concini-Procesi associahedra. These results will be used in the sequel to this paper to give a monodromic description of the quantum Weyl group operators of an affine Kac-Moody algebra, extending the one obtained by the second author for a semisimple Lie algebra.Comment: 63 pages. Exposition in sections 1 and 4 improved. Material added: definition of a split pair of Lie bialgebras (sect. 5.2-5.5), 1-jet of the relative twist (5.20), PROP description of the Verma modules L_-,N*_+ (7.6), restriction to Levi subalgebras (8.4), D-structures on Kac-Moody algebras (9.1

Inference for Partially Observed Multitype Branching Processes and Ecological Applications

Multitype branching processes with immigration in one type are used to model the dynamics of stage-structured plant populations. Parametric inference is first carried out when count data of all types are observed. Statistical identifiability is proved together with derivation of consistent and asymptotically Gaussian estimators for all the parameters ruling the population dynamics model. However, for many ecological data, some stages (i.e. types) cannot be observed in practice. We study which mechanisms can still be estimated given the model and the data available in this context. Parametric inference is investigated in the case of Poisson distributions. We prove that identifiability holds for only a subset of the parameter set depend- ing on the number of generations observed, together with consistent and asymptotic properties of estimators. Finally, simulations are performed to study the behaviour of the estimators when the model is no longer Poisson. Quite good results are obtained for a large class of models with distributions having mean and variance within the same order of magnitude, leading to some stability results with respect to the Poisson assumption.Comment: 31 pages, 1 figur