  We introduce a deformation of the affine Hecke algebra of type GL which
describes the commutation relations of the divided difference operators found
by Lascoux and Schutzenberger and the multiplication operators. Making use of
its representation we construct an integrable stochastic particle system. It is
a generalization of the q-Boson system due to Sasamoto and Wadati. We also
construct eigenfunctions of its generator using the propagation operator. As a
result we get the same eigenfunctions for the (q, \mu, \nu)-Boson process
obtained by Povolotsky.
