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We introduce a deformation of the affine Hecke algebra of type GL whichdescribes the commutation relations of the divided difference operators foundby Lascoux and Schutzenberger and the multiplication operators. Making use ofits representation we construct an integrable stochastic particle system. It isa generalization of the q-Boson system due to Sasamoto and Wadati. We alsoconstruct eigenfunctions of its generator using the propagation operator. As aresult we get the same eigenfunctions for the (q, \mu, \nu)-Boson processobtained by Povolotsky.

A deformation of affine Hecke algebra and integrable stochastic particle system