Daniel Arnaudon

Spectrum and Bethe Ansatz Equations for the U_{q} {\left( {gl(\mathcal{N})} \right)} Closed and Open Spin Chains in any Representation

Abstract.We consider the N-site

ON CASIMIR'S GHOST

U_{q} {\left( {gl(\mathcal{N})} \right)}

Correspondence between conformal field theory and Calogero-Sutherland model

integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to determine the spectrum and the corresponding Bethe ansatz equations for the general case, where each site of the spin chain is associated to any representation of

Spectral Decomposition and Baxterization of Exotic Bialgebras and Associated Noncommutative Geometries

U_{q} {\left( {gl(\mathcal{N})} \right)}.

Bethe Ansatz equations and exact S matrices for the osp(M |2n) open super spin chain.

In the case of open spin chain, we study finite dimensional representations of the quantum reflection algebra, and prove in full generality that the pseudo-vacuum is a highest weight of the monodromy matrix.For these two types of spin chain, we study the (generalized) “algebraic” fusion procedures, which amount to construct the quantum contraction and the Sklyanin determinant for the