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In a previous paper a multi-species version of the q-Boson stochasticparticle system is introduced and the eigenfunctions of its backward generatorare constructed by using a representation of the Hecke algebra. In this articlewe prove a formula which expresses the eigenfunctions by means of theq-deformed bosonic operators, which are constructed from the L-operator ofhigher rank found in the recent work by Garbali, de Gier and Wheeler. TheL-operator is obtained from the universal R-matrix of the quantum affinealgebra of type A_{r}^{(1)} by the use of the q-oscillator representation. Thusour formula may be regarded as a bridge between two approaches to studyingintegrable stochastic systems by means of the quantum affine algebra and theaffine Hecke algebra.

On the eigenfunctions for the multi-species q-Boson system