We established a correspondence among simple objects of the relative commutant of a full fusion subcategory in a larger fusion category in the sense of Drinfel'd, irreducible half-braidings of objects in the larger fusion category with respect to the fusion subcategory, and minimal central projections in the relative tube algebra generalizing Ocneanu's tube algebra. Based on this, we explicitly compute certain relative Drinfel'd commutants of fusion categories arising from alpha-induction for braided subfactors. We also presented examples arising from chiral conformal field theory.