Mathematical Sciences: Unification of Integrable Systems

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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.