TL;DR
This paper revisits multi-field reductions of KP and super-KP hierarchies using coset construction, highlighting how Hamiltonian densities form a coset algebra within a Poisson brackets framework.
Contribution
It introduces a coset-based perspective on multi-field reductions of KP hierarchies, expanding understanding of their algebraic structure.
Findings
Hamiltonian densities belong to a coset algebra
The approach applies to non-purely differential Lax operators
Provides new insights into the algebraic structure of KP reductions
Abstract
In this talk the class of multi-fields reductions of the KP and super-KP hierarchies (leading to non-purely differential Lax operators) is revisited from the point of view of coset construction. This means in particular that all the hamiltonian densities of the infinite tower belong to a coset algebra of a given Poisson brackets structure.
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