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

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...

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Bibliographic Details
Published inFunkcialaj Ekvacioj Vol. 61; no. 3; pp. 349 - 376
Main Author Takeyama, Yoshihiro
Format Journal Article
LanguageEnglish
Published Tokyo Division of Functional Equations, The Mathematical Society of Japan 2018
Japan Science and Technology Agency
Subjects
Affine Hecke algebra
Algebra
Deformation
Eigenvectors
Integrable system
Operators (mathematics)
Quantum group
Representations
Stochastic process
Stochastic systems
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Summary: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.
ISSN:0532-8721
DOI:10.1619/fesi.61.349