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Integration of quantum many-body problems by affine Knizhnik- Zamolodchikov equations. (English) Zbl 0806.35146

Summary: An equivalence of the affine analogues of Knizhnik-Zamolodchikov and Dunkl equations is established for arbitrary root systems. As a corollary, an isomorphism is obtained from the solutions of the above KZ equations (in the induced representations of Hecke algebras) to the eigenfunctions for the corresponding matrix quantum Calogero-Sutherland operators, which generalizes the Matsuo map.

MSC:

35Q40 PDEs in connection with quantum mechanics
81V70 Many-body theory; quantum Hall effect
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