Calogero–Moser eigenfunctions modulo \(p^s\)

In this note we use the Matsuo–Cherednik duality between the solutions to the Knizhnik–Zamolodchikov (KZ) equations and eigenfunctions of Calogero–Moser Hamiltonians to get the polynomial \(p^s\) $p^s$ -truncation of the Calogero–Moser eigenfunctions at a rational coupling constant. The truncation procedure uses the integral representation for the hypergeometric solutions to KZ equations. The \(s\rightarrow \infty \) $s\to \infty$ limit to the pure p-adic case has been analyzed in the \(n=2\) $n=2$ case.