On the Eigenfunctions for the Multi-species <i>q</i>-Boson System
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In a previous paper a multi-species version of the <i>q</i>-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 <i>q</i>-deformed bosonic operators, which are constructed from the <i>L</i>-operator of higher rank found in the recent work by Garbali, de Gier and Wheeler. The <i>L</i>-operator is obtained from the universal <i>R</i>-matrix of the quantum affine algebra of type <i>A</i><sub><i>r</i></sub><sup>(1)</sup> by the use of the <i>q</i>-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.
- Funkcialaj Ekvacioj
Funkcialaj Ekvacioj 61(3), 349-376, 2018
Division of Functional Equations, The Mathematical Society of Japan