Mathematical Sciences: Unification of Integrable Systems

9404290可积系统的多德统一该方案通过仿射李代数的表示理论来研究可积系统的分类。该方案旨在利用水平1无限秩仿射李代数的表示理论，对通过Kruskal机制可积的方程进行分类。由极大Heisenberg子代数决定的经典有限秩仿射李代数的正则表示可以与无限秩仿射李代数的表示的约化联系在一起，许多不同的可积系统(PDE，ODE，微分差分等)也是如此。它们是通过在每个正则表示中的详尽构造来发现的。

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.