POWRE: Representations of Quantum Affine Algebras and Integrable Models

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9870550 Kedem Integrable quantum field theories are related to certain integrable lattice models on the infinite lattice through the notion of the space of states, which carries the structure of an affine algebra representation. The PI will use the structure of representations of certain affine algebra's to define massive integrable field theories in terms of these representations. Previous results of the PI and co-authors suggest the existence of a certain fermionic construction of the coset representations of the Virasoro algebra corresponding to minimal models in conformal field theory and its deformations. This construction will reflect the role of the representation as the space of states of a particular massive deformation of a conformal field theory. The PI plans to apply results about the space of states of integrable lattice models to supply such a construction. This will give a representation theoretical proof of the fermionic character formulas. Kedem will use these results to find the representations corresponding to massive integrable models and its relation to non-critical RSOS models, and the role of deformed Virasoro algebra in such theories. In addition the PI will apply representation theoretical methods to find solutions to certain longstanding problems in the theory of lattice integrable models, associated with the chiral Potts model.