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

2023/04/12 by Kac, Victor, van de Leur, Johan · 4 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2304.05737

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 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.

Cited by

• Transformations of the 2-component BKP tau functions
• Tau functions of the constrained matrix KP hierarchy
• The two--component discrete KP hierarchy
• One reduction of the modified Toda hierarchy

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