POWRE: Representations of Quantum Affine Algebras and Integrable Models

Kedem可积量子场论通过状态空间的概念与无限格上的某些可积点阵模型相联系，状态空间具有仿射代数表示的结构。PI将使用某些仿射代数的表示结构来根据这些表示定义大量可积场论。PI及其合作者先前的结果表明，在共形场论及其变形中，Virasoro代数的协集表示的某种费米子构造对应于最小模型。这种构造将反映表征作为共形场论中特定大规模变形的状态空间的作用。PI计划应用关于可积晶格模型的状态空间的结果来提供这样的构造。这将给出费米子特征公式的一个表示理论证明。Kedem将利用这些结果找到大量可积模型及其与非临界RSOS模型的关系对应的表示，以及变形Virasoro代数在这些理论中的作用。此外，PI将应用表示理论方法来解决与手性波茨模型相关的晶格可积模型理论中某些长期存在的问题。

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.