Quasi exactly solvable operators and Lie superalgebras

Abstract

Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. An example of a Hamiltonian possessing such a hidden algebra is analyzed.

8 Revtex pages, 1 PS-figures; Section IV extended, reference added

References in corpus (5)

• Energy Reflection Symmetry of Lie-Algebraic Problems: Where the Quasiclassical and Weak Coupling Expansions Meet
• Quasi Exactly Solvable 2$\times$2 Matrix Equations
• Quasi Exactly Solvable NxN-Matrix Schroedinger Operators
• The hidden symmetry algebras of a class of quasi-exactly solvable multi dimensional operators
• Realizations of the Lie superalgebra q(2) and applications

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