A deformation of affine Hecke algebra and integrable stochastic particle system

TL;DR

This paper introduces a new deformation of the affine Hecke algebra of type GL, enabling the construction of an integrable stochastic particle system that generalizes the q-Boson system and provides explicit eigenfunctions.

Contribution

It presents a novel algebraic deformation and constructs an associated integrable stochastic particle system with explicit eigenfunctions, extending previous models.

Findings

Constructed a new integrable stochastic particle system.

Derived explicit eigenfunctions for the system's generator.

Generalized the q-Boson system to a broader class.

Abstract

We introduce a deformation of the affine Hecke algebra of type GL which describes the commutation relations of the divided difference operators found by Lascoux and Schutzenberger and the multiplication operators. Making use of its representation we construct an integrable stochastic particle system. It is a generalization of the q-Boson system due to Sasamoto and Wadati. We also construct eigenfunctions of its generator using the propagation operator. As a result we get the same eigenfunctions for the (q, \mu, \nu)-Boson process obtained by Povolotsky.