Diagonalization of the infinite q-boson system

Abstract

We present a hierarchy of commuting operators in Fock space containing the q-boson Hamiltonian on $\mathbb{Z}$ and show that the operators in question are simultaneously diagonalized by Hall-Littlewood functions. As an application, the n-particle scattering operator is computed.

13 pages

References in corpus (3)

• 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

Cited by in corpus (5)

• Spectral theory for the q-Boson particle system
• Orthogonality of Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove
• A q-difference Baxter's operator for the Ablowitz-Ladik chain
• Quantum Integrals for a Semi-Infinite $q$-Boson System with Boundary Interactions
• Boundary Interactions for the Semi-Infinite q-Boson System and Hyperoctahedral Hall-Littlewood Polynomials