# 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}
}
• Y. Takeyama
• Published 8 July 2014
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
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
• 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
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
• 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
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
• 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
• 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
• Mathematics
Communications 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
• 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

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
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)
• Mathematics
Compositio 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
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
• 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
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
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