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

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