  We show that quantum Schur-Weyl duality leads to Markov duality for a variety
of asymmetric interacting particle systems. In particular, we consider three
cases:
  (1) Using a Schur-Weyl duality between a two-parameter quantum group and a
two-parameter Hecke algebra from arXiv:math/0108038, we recover the Markov
self-duality of multi-species ASEP previously discovered in arXiv:1605.00691
and arXiv:1606.04587.
  (2) From a Schur-Weyl duality between a co-ideal subalgebra of a quantum
group and a Hecke algebra of type B arXiv:1609.01766, we find a Markov duality
for a multi-species open ASEP on the semi-infinite line. The duality functional
has not previously appeared in the literature.
  (3) A "fused" Hecke algebra from arXiv:2001.11372 leads to a new process,
which we call braided ASEP. In braided ASEP, up to m particles may occupy a
site and up to m particles may jump at a time. The Schur-Weyl duality between
this Hecke algebra and a quantum group lead to a Markov duality. The duality
function had previously appeared as the duality function of the multi-species
ASEP(q,m/2) arXiv:1605.00691 and the stochastic multi-species higher spin
vertex model arXiv:1701.04468.
