# A deformation of affine Hecke algebra and integrable stochastic particle system

@article{Takeyama2014ADO, title={A deformation of affine Hecke algebra and integrable stochastic particle system}, author={Yoshihiro Takeyama}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2014}, volume={47} }

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 Schützenberger 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…

## 25 Citations

### Completeness of the Bethe Ansatz for an Open q -Boson System with Integrable Boundary Interactions

- Mathematics
- 2018

. We employ a discrete integral-reﬂection representation of the double aﬃne Hecke algebra of type C ∨ C at the critical level q = 1, to endow the open ﬁnite q -boson system with integrable boundary…

### Algebraic construction of multi-species q-Boson system

- Mathematics
- 2015

We construct a stochastic particle system which is a multi-species version of the q-Boson system due to Sasamoto and Wadati. Its transition rate matrix is obtained from a representation of a…

### Integrable Structure of Multispecies Zero Range Process

- Mathematics
- 2017

We present a brief review on integrability of multispecies zero range process in one-dimension introduced recently. The topics range over stochastic $R$ matrices of quantum affine algebra…

### Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice

- Mathematics
- 2016

We introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in finite lattice. We introduce the $L$-operator related…

### Completeness of the Bethe Ansatz for an Open $$\varvec{q}$$q-Boson System with Integrable Boundary Interactions

- Mathematics
- 2018

We employ a discrete integral-reflection representation of the double affine Hecke algebra of type $$C^\vee C$$C∨C at the critical level $$\text {q}=1$$q=1, to endow the open finite q-boson system…

### Quantum Integrals for a Semi-Infinite q-Boson System with Boundary Interactions ?

- Mathematics
- 2015

We provide explicit formulas for the quantum integrals of a semi-infiniteq-boson system with boundary interactions. These operators and their commutativity are deduced from the Pieri formulas for a…

### A New Generalisation of Macdonald Polynomials

- MathematicsCommunications in Mathematical Physics
- 2017

We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters (q, t) and polynomial in a further two parameters (u, v). We evaluate…

### A New Generalisation of Macdonald Polynomials

- Mathematics
- 2016

We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters (q, t) and polynomial in a further two parameters (u, v). We evaluate…

## References

SHOWING 1-10 OF 17 REFERENCES

### A discrete analogue of periodic delta Bose gas and affine Hecke algebra

- Mathematics
- 2012

We consider an eigenvalue problem for a discrete analogue of the Hamiltonian of the non-ideal Bose gas with delta-potentials on a circle. It is a two-parameter deformation of the discrete Hamiltonian…

### Unitary representations of affine Hecke algebras related to Macdonald spherical functions

- Mathematics
- 2012

### Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

- Physics, Mathematics
- 2006

We introduce an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials. The corresponding (finite-dimensional)…

### Spectral theory for the $q$-Boson particle system

- MathematicsCompositio Mathematica
- 2014

Abstract We develop spectral theory for the generator of the $q$-Boson (stochastic) particle system. Our central result is a Plancherel type isomorphism theorem for this system. This theorem has…

### On the integrability of zero-range chipping models with factorized steady states

- Mathematics
- 2013

The conditions of the integrability of general zero range chipping models with factorized steady states, which were proposed in Evans et al (2004 J. Phys. A: Math. Gen. 37 L275), are examined. We…

### Exact results for one-dimensional totally asymmetric diffusion models

- Physics
- 1998

Several types of totally asymmetric diffusion models with and without exclusion are considered. For some models, conditional probabilities of finding N particles on lattice sites at time t with…

### The $(q,\mu,\nu)$-Boson process and $(q,\mu,\nu)$-TASEP

- Mathematics
- 2014

We prove a intertwining relation (or Markov duality) between the $(q,\mu,\nu)$-Boson process and $(q,\mu,\nu)$-TASEP, two discrete time Markov chains introduced by Povolotsky. Using this and a…

### On the Plancherel Formula for the (Discrete) Laplacian in a Weyl Chamber with Repulsive Boundary Conditions at the Walls

- Mathematics
- 2004

It is known from early work of Gaudin that the quantum system of n Bosonic particles on the line with a pairwise delta-potential interaction admits a natural generalization in terms of the root…