A deformation of affine Hecke algebra and integrable stochastic particle system

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, μ, ν)-Boson process obtained by Povolotsky.

arXiv comment18 pages, no fugure

References in corpus (4)

• On integrability of zero-range chipping models with factorized steady state
• Spectral theory for the q-Boson particle system
• Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle
• Unitary representations of affine Hecke algebras related to Macdonald spherical functions

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• A $q$-boson representation of Zamolodchikov-Faddeev algebra for stochastic $R$ matrix of $U_q(A_n^{(1)})$
• Integrable Structure of Multispecies Zero Range Process
• Quantum Integrals for a Semi-Infinite $q$-Boson System with Boundary Interactions
• Density and current profiles in $U_q(A_2^{(1)})$ zero range process
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• Parameter Permutation Symmetry in Particle Systems and Random Polymers
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