Mathematical Sciences: Unification of Integrable Systems

9404290可积系统的多德统一该提案通过仿射李代数的表示理论研究可积系统的分类。该提案旨在分类方程，可通过Kruskal机制，通过使用表示理论的水平1无限秩仿射李代数。经典有限秩仿射李代数的标准表示由极大海森堡子代数确定，可以与无限秩仿射李代数的表示的约化相联系，许多不同的可积系统（PDE，ODE，微分差分等）也是如此。 其通过在每个规范表示内的穷举构造来找到。

9404290 Dodd Unification of integrable SystemsThe proposal investigates the classification of integrable systems through the representation theory of affine Lie algebras. The proposal intends to classify equations, integrable through the Kruskal mechanism, by using the representation theory of level 1 infinite rank affine Lie algebras. Canonical representations of the classical finite rank affine Lie algebras, determined by maximal Heisenberg subalgebras, can be associated with reductions of the representations of the infinite rank affine Lie algebras, as can many diverse integrable systems (pde, ode, differential-difference etc.) which are found by exhaustive construction within each canonical representation.