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

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

1996-12-20

arxiv.org/abs/solv-int/9612009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

38 pages, latex

Scientific paper

10.1007/s002200050133

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 A(2). The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitely. The results are related to the theory of quasi exactly solvable equations.

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