We describe a new generalisation of the quantum harmonic oscillator, which involves a deformation parameter q and a modification parameter nu, and its Fock space F(q,nu). We discuss spectrum generating algebras and hidden supersymmetry properties of F(q,nu) and of various limiting cases, such as the Calogero model.

A large class of vertex models are defined on a 2×N lattice with toroidal boundary conditions in such a way that exact solutions can be performed by straightforward analysis and non-trivial phase structure is exhibited.