Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras

Johan van de Leur; Victor Kac

Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras

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arxiv 2304.05737 v1 pith:2P6FSJUA submitted 2023-04-12 math-ph hep-thmath.MPmath.RTnlin.SI

Victor Kac , Johan van de Leur This is my paper · ORCID

classification math-phhep-thmath.MPmath.RTnlin.SI

keywords multicomponenttypealgebrasassociatedclassesclassicalconjugacygroups

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This, to a large extent, expository paper, describes the theory of multicomponent hierarchies of evolution equations of XKP type, where X=A, B, C or D, and AKP=KP, and their reductions, associated to the conjugacy classes of the Weyl groups of classical Lie algebras of type X. As usual, the main tool is the multicomponent boson-fermion correspondence, which leads to the corresponding tau-functions, wave functions, dressing operators and Lax operators.

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Elliptic solutions to matrix CKP equation
nlin.SI 2026-08 conditional novelty 6.0 of 10

Elliptic solutions of the matrix CKP equation have pole dynamics described by a first-order system, equations (47)-(48), generalizing the scalar CKP result.

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