Abstract
A wide class of integrable quantum-optical models with Gi-invariant Hamiltonians H is described in the form when H are linear functions in generators of the polynomial Lie algebras supd(2) and Hilbert spaces L(H) of quantum states are decomposed in direct sums of supd(2)-irreducible subspaces. This yields exact and approximate methods of solving physical problems as well as new (supd(2)-cluster) quasiclassics in original models.
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