  We obtain orthogonal polynomial self-duality functions for multi-species
version of the symmetric exclusion process (SEP$(2j)$) and the independent
random walker process (IRW) on a finite undirected graph. In each process, we
have $n>1$ species of particles. In addition, we allow up to $2j$ particles to
occupy each site in the multi-species SEP$(2j)$. The duality functions for the
multi-species SEP$(2j)$ and the multi-species IRW come from unitary
intertwiners between different $*$-representations of the special linear Lie
algebra $\mathfrak{sl}_{n+1}$ and the Heisenberg Lie algebra $\mathfrak{h}_n$,
respectively. The analysis leads to multivariate Krawtchouk polynomials as
orthogonal duality functions for the multi-species SEP$(2j)$ and homogeneous
products of Charlier polynomials as orthogonal duality functions for the
multi-species IRW.
