2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186895Motivated by Haldane's exclusion statistics, we construct creation and annihilation operators for $g$-ons using a bosonic algebra. We find that $g$-ons appear due to the breaking of a descrete symmetry of the original bosonic system. This symmetry is intimately related to the braid group and we demonstrate a link between exclusion statistics and fractional statistics.10 pages, ReVTeX 3.0Condensed MatterHigh Energy Physics - TheoryQuantum AlgebraQuantum PhysicsTurning Bosons into Fermions: Exclusion Statistics, Fractional Statistics and the Simple Harmonic Oscillatortext