On adelic model of boson Fock space

Neretin Yuri

Published 2006-06-15, updated 2016-05-09Version 2

We construct a canonical embedding of the Schwartz space on $R^n$ to the space of distributions on the adelic product of all the $p$-adic numbers. This map is equivariant with respect to the action of the symplectic group $Sp(2n, Q)$ over rational numbers and with respect to the action of the rational Heisenberg group.