Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations

Abstract:The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra . The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitly. The results are related to the theory of quasi exactly solvable equations.