Representations of the $S_N$-Extended Heisenberg Algebra and Relations Between Knizhnik-Zamolodchikov Equations and Quantum Calogero Model

Abstract

We discuss lowest-weight representations of the $S_N$-Extended Heisenberg Algebras underlying the $N$-body quantum-mechanical Calogero model. Our construction leads to flat derivatives interpolating between Knizhnik-Zamolodchikov and Dunkl derivatives. It is argued that based on these results one can establish new links between solutions of the Knizhnik-Zamolodchikov equations and wave functions of the Calogero model.