Mathematical Sciences: Unification of Integrable Systems

9404290 Dodd可积系统的统一本文通过仿射李代数的表示理论研究了可积系统的分类。利用1阶无限阶仿射李代数的表示理论，拟对可积的Kruskal机制下的方程组进行分类。经典有限阶仿射李代数的正则表示，由极大海森堡子代数决定，可以与无限阶仿射李代数的表示的约简相关联，正如许多不同的可积系统（pde, ode，微分-差分等）可以通过在每个正则表示内的穷举构造找到。

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.