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.

We added an explanation of the relation between our result and the previous results due to Borodin, and Motegi and Sakai in Section 5.1

References in corpus (2)

• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Algebraic construction of multi-species q-Boson system

Cited by in corpus (3)

• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula