  In previous work a higher rank generalization $R(n)$ of the Racah algebra was
defined abstractly. The special case of rank one encodes the bispectrality of
the univariate Racah polynomials and is known to admit an explicit realization
in terms of the operators associated to these polynomials. Starting from the
Dunkl model for which we have an action by $R(n)$ on the Dunkl-harmonics, we
show that connection coefficients between bases of Dunkl-harmonics
diagonalizing certain Abelian subalgebra are multivariate Racah polynomials. By
lifting the action of $R(n)$ to the connection coefficients, we identify the
action of the Abelian subalgebras with the action of the Racah operators
defined by J. S. Geronimo and P. Iliev. Making appropriate changes of basis one
can identify each generator of $R(n)$ as a discrete operator acting on the
multivariate Racah polynomials.
