On the Eigenfunctions for the Multi-species q-Boson System

Abstract

In a previous paper a multi-species version of the q-Boson stochastic particle system is introduced and the eigenfunctions of its backward generator are constructed by using a representation of the Hecke algebra. In this article we prove a formula which expresses the eigenfunctions by means of the q-deformed bosonic operators, which are constructed from the L-operator of higher rank found in the recent work by Garbali, de Gier and Wheeler. The L-operator is obtained from the universal R-matrix of the quantum affine algebra of type A_r⁽¹⁾ by the use of the q-oscillator representation. Thus our formula may be regarded as a bridge between two approaches to studying integrable stochastic systems by means of the quantum affine algebra and the affine Hecke algebra.