On the Eigenfunctions for the Multi-species <i>q</i>-Boson System

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  • 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 Ar(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.

Journal

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 61 (3), 349-376, 2018

    Division of Functional Equations, The Mathematical Society of Japan

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