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

Abstract

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 \(p^s\)-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 \(s\rightarrow \infty \) limit to the pure p-adic case has been analyzed in the \(n=2\) case.