On the relations between osp(2,2) and the quasi exactly solvable systems

Brihaye, Yves; Giller, Stefan; Kosinski, Piotr

On the relations between osp(2,2) and the quasi exactly solvable systems

Authors

Brihaye, Yves

Giller, Stefan

Kosinski, Piotr

Description

By taking a product of two sl(2) representations, we obtain the differential operators preserving some space of polynomials in two variables. This allows us to construct the representations of osp(2,2) in terms of matrix differential operators in two variables. The corresponding operators provide the building blocks for the construction of quasi exactly solvable systems of two and four equations in two variables. Some generalisations are also sketched. The peculiar labelling used for the generators allows us to elaborate a nice deformation of osp(2,2). This gives an appropriate basis for analyzing the quasi exactly solvable systems of finite difference equations.
14 pages, latex