  We establish a correspondence among simple objects of the relative commutant
of a full fusion subcategory in a larger fusion category in the sense of
Drinfeld, 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. Based on this, we explicitly compute certain relative
Drinfeld commutants of fusion categories arising from $\alpha$-induction for
braided subfactors. We present examples arising from chiral conformal field
theory.
