Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras
Victor G. Kač, Johan van de Leur
Abstract
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 with 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.
Topics & Concepts
Conjugacy classMathematicsType (biology)Pure mathematicsLie algebraWeyl groupLie theoryLie groupRepresentation theoryFundamental representationAlgebra over a fieldLie conformal algebraAdjoint representation of a Lie algebraBiologyWeightEcologyNonlinear Waves and SolitonsAlgebraic structures and combinatorial modelsAdvanced Algebra and Geometry