2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61851We attach representations to non-symplectic stratum in the characteristic set of real vector fields. This leads to Schrodinger operators. The analysis of the solutions of these Schrodinger equations allows us to construct smooth, non-analytic solutions of the sub-elliptic operator formed by taking sums of squares of the real vector fields.34 pages, typos correctedAnalysis of PDEsRepresentation Theorytext