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Brihaye, Yves; Hartmann, Betti

Quasi exactly solvable operators and Lie superalgebras. (English) Zbl 1006.81018

Phys. Lett., A 306, No. 5-6, 291-295 (2003).
Summary: 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.

Cited in 1 Document

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)

Keywords:

direct polynomial-ring sum preservation; osp\((2,2)\) algebra representations; Hamiltonian
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References:

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