  In the spirit of the Schur-Weyl duality, we study the connections between the
Racah algebra and the centralizers of tensor products of three (possibly
different) irreducible representations of su(2). As a first step we show that
the Racah algebra always surjects onto the centralizer. We then offer a
conjecture regarding the description of the kernel of the map, which depends on
the irreducible representations. If true, this conjecture would provide a
presentation of the centralizer as a quotient of the Racah algebra. We prove
this conjecture in several cases. In particular, while doing so, we explicitly
obtain the Temperley-Lieb algebra, the Brauer algebra and the one-boundary
Temperley-Lieb algebra as quotients of the Racah algebra.
